from SkyBooksUSA Website

 

 

Contents

  1. Space - Time

  2. Is time Travel Possible?

  3. Time travel on Agenda

  4. Why Time Travel is Possible

  5. Time Travel for beginners

 

 

 

 

 

 

 

 

 

 

 




 


 Space - Time

by Kalen J. Craig
 


SPACE

Einstein said that three dimensional space may be curved and could be closed into a sphere or a torus. It would likely have a radius of curvature of approximately: RE = GMuc2 = 6.4 x 1026 cm, where G is the constant of gravity and Mu is the mass of the universe.

In 1926 two scientists Theodore Kaluza and Oskar Klein suggested that electromagnetic theory could be explained if space had a fourth dimension composed of a multitude of compacted space bubbles whose radii of curvature approximate the Planck length: d = √(hG/c3) = 1.61 x 10-33 cm. A Kaluza-Klein compacted space bubble is represented by Planck’s constant of action h. Which is the unit of angular momentum, h = mcy, where mc is the electron momentum and y is the Compton wavelength of an electron.

Planck=s action represents one rotation cycle of an electron. Each such cycle of action is thought to produce a compact space bubble that is emitted from an electron to translate through three-space at less than c. Such action bubbles have a slight mass so that an acceleration or deceleration of the bubble flow, represents an electrostatic force. Motion of the source electrons and hence the flow produces an orthogonal magnetic field. An acceleration or oscillation of the charge source generates an electromagnetic field that moves at c.

Eugene and I agree with this and go a bit further. We assume that the four fundamental forces: the electromagnetic and gravitational forces plus the strong and weak nuclear forces can each be represented by a compacted space dimension. This makes physical space seven dimensional.

We further assume that these compacted spaces (sometimes called Calabi-Yau space) make physical space into a super fluid ether.

We also assume that the ether fluid produces two independent flows. One which we call charge space is a manifestation of the flow properties of the electrostatic and strong force compacted dimensions. We call these compacted bubbles geoids. They are probably two dimensional toruses (doughnut shaped surfaces).

Charge space geoids flow out of positive charge spinning one way and out of negative charge spinning the other. The flows start out at near velocity c inside the particle expand out through the particle and decelerate generating an all prevailing electrostatic force field. This field is the charge space (ether). Whenever the flows get together they cancel creating an attraction between opposite charges.

We call the other ether flow gravity space. It may exists as very tiny three dimensional blobs which are the compacted space bubbles from gravity and the weak nuclear force. The size of these blobs could approximate the gravitational radius of an electron: s = Gm/c2 = 6.75 x 10-56 cm, where the m, in this case, is the mass of an electron. We suspect these tiny geons are Higgs particles, with a mass something like 10-191 grams.

The assumption that space is composed of compacted space bubbles with a slight mass accords with quantum mechanics; because, empty space is commonly thought to generate quantum fluctuations that give it a small energy or mass.

The mass of space could generate a positive cosmological constant (repulsion) that, like Einstein suggested in his 1916 general theory, could balance the attraction of gravity, and keep the radius of 3-space curvature constant. (See Steven Weinbergs, "Dreams of a Final Theory", page 224, Random House, 1992).

It is not usually recognized that the observed redshift of light from distant sources could be due to the collapse of the time dimensions, of space-time, as well as it can be from the generally assumed expansion of 3-space. (see Figures 7&8 from our book the Kalen Universe, on our web site the, "kalenuniverse.com".

If the reader wishes to follow our concept of space flows in more detail, he can check out the summary link or the link to chapter 6 of our book in the above web site.

He would see how and why gravity space geons appear instantly out of wormholes between matter and antimatter galaxies; this causes an outer space repulsion (Einstein’s cosmological constant) between opposite types of matter. This repulsion separates the universe into equal parts of matter and antimatter, and helps explain the missing mass dark matter problem for cosmologists.

In brief: gravity space geons in outer space converge and accelerate. The acceleration produces gravity and the convergence produces mass particles. At the center of each particle the flow at velocity c produces a black wormhole, through which we postulate that the geons instantly transfer to a mirror image of the particle. This image occurs at another place in space-time which we call the shadow world. However, space and time does not exist in the wormhole between the particle and its mirror image. Hence these images are simply a continuance of the real world particles in an unseen shadow world.

The fast moving geons at the center of the shadow world image particles expand outward and decelerate producing a weak nuclear force in the particle. The weak force is similar to the electromagnetic force and helps produce particle decays. The deceleration reduces the G flow to zero near the particle surface. We postulate the zero motion generates a wormhole that allows the stoped geons to transfer instantly out through macro space to an interface between matter and antimatter galaxies.

Again, the geon flows start in outer space at zero velocity then converge and accelerate down toward fermion particles. The acceleration creates gravity and the convergence gives inertial mass to the shadow world particles. Geons spinning one way converge toward matter while those spinning the other converge toward antimatter.


TIME

What is time? Time is mysterious and hard to define. In this paper we will limit our discussion to physical time, because psychological time seems even more mysterious.

Dirk Brower of MIT (who consulted with Kalen when he worked at the Naval Research Laboratory) characterized time as the great undefined variable of physics.

We have also heard time defined as that which is measured by a clock. A clock measures some steady motion, or change, such as the evolution or decay of a physical quantity; like mass, energy, pressure, entropy and etc. The change of the quantity could be in space as position, size or shape.

Einstein suggested that a light beam bouncing back and forth between two mirrors would be a perfect clock. A light beam is a perfectly steady motion.

Motion usually implies the translation of mass particles through space, but if the motion is a light beam no mass is involved. Light is just an oscillatory motion of space. So a unit of time for this motion would be a unit of space. Likewise, if as we say, mass can be defined as the convergence of space toward a wormhole in space, then again a unit of motion or time is a unit of space. This may seem a bit vague so we will give one more example.

We propose that: all motion is wave motion.

In order to explain this concept, we first refer to the basic postulate #2 of the KALEN UNIVERSE: That a condition of zero time opens a wormhole, which is an instantaneous path to another location in space-time (see the link to chapter 3 (Postulates) of our book in the kalenuniverse.com web site).

In relativity theory, zero time occurs at the velocity c of light. We assume in our #2 postulate that zero time also occurs at zero velocity (no motion no time).

Electromagnetic waves move at c and have zero time along the line of motion. However, orthogonal to the line of motion, the electric and magnetic fields move (oscillate) at less than c. When, however, a magnetic or electric field goes through a maximum there is a moment of zero motion. This occurs for any sine wave motion. Wormholes can occur at these wave peaks.

Electromagnetic waves expand spherically as retarded waves from a charge source. Under Maxwell=s equations normal (retarded) waves are received after they are emitted. Whereas, his advanced waves have negative time and, we predict, they converge through wormholes and are received at the same time as they start. You see that, when a wave front reaches a target charge (electron) it triggers a wormhole all along the wave front. The retarded wave collapses instantly through the wormhole (as an advanced wave) onto the target charge. One can often plot this expansion and collapse as a straight line from the source to the target. You see a photon does not move as a particle along a line but rather moves as a wave function from source to target.

The two hole experiment of quantum mechanics shows that not only do bosons (photons) travel as waves but so do fermion particles such as electrons. See our article Quantum Weirdness. This paper along with Questionable Cosmological Assumptions, are good background articles to read along with the present paper.

Inertial particles (fermions) contain both charge and mass. They are both electromagnetic and gravitational, so are composed of both electromagnetic and gravity waves.

Eugene and I postulate that these tiny gravity waves are a sub harmonic of electromagnetic waves, but are much, much weaker, smaller and more complex. A mathematical theory of such tiny gravity waves has not been written.

Our suggestion is a new action constant k which we call the kalen. The constant k = mcd where mc is the electron momentum and d is the Planck length: d = √(hG/c3) = 1.61 x 10-33 cm, where h is the Planck unit of angular momentum and G is the constant of gravity. This k unit should give a sub harmonic of quantum theory for gravity waves. This would reduce the indeterminacy of quantum theory and explain Einstein=s hidden variables.

However, a mathematical beginning for a theory of gravity waves (through the M theory of super strings) is on the horizon. Incidentally, in string theory all the particles are generated by (composed of) vibrations of tiny strings of space or of membranes or blobs such as our geoids or geons.

Any mass such as the earth is composed of quantum particles (fermions) which are just complex wave packet particles, that move as waves much like photons move. They just make more starts and stops and so travel slower than photons. Fermion particles do not need a target to move to. They just reproduce themselves in time as they move along.

Our all motion is wave motion idea, with its instantly collapsing advanced waves and multiple micro starts and stops, may seem far out, but is actually quite simple. When it is compared to the concept of the various boson messenger particles of quantum mechanics.

Boson messenger particles can be better visualized as flow properties of space. That is, a force field between two objects is easily visualized as due to the appearance or disappearance of space between the objects.

If all motion is wave motion and time is motion then again, the unit of time should be a unit of waves (space).

In the first section of this article (SPACE) we proposed two compacted units of space. One which we call geoids for charge (electromagnetic) space. The other we call geons for gravity space. The geoids are unit electromagnetic cycles (from one electron) given by Planck=s constant of action (angular momentum): h = mcy where y is the Compton wavelength; of an electron. A geon is a unit gravity cycle from one electron given by kalen=s constant of action k = mcd and, as we said, d is the Planck length.

If the basic increments of space and time are the same, then geoids and geons are also basic units of time.

However, time dimensions are not quite the same as space dimensions.

In general relativity the time dimension or dimensions are orthogonal to the space dimensions. This is indicated mathematically by multiplying the time dimensions by √(-1). Multiplying by -1 gives a 180º rotation and multiplying by √(-1) gives a 90º rotation.

Both; space and time are compounded from the basic units of action: the geoids h and the geons k. Gene and I assume that h and k are the ultimate units of existence and are more basic than length, time or mass, even though, h and k appear to have the math dimensions of ML2/T. Consequently, trying to measure the length, time or mass of quantum particles in terms of h and k leads to Heisenberg=s uncertainty principle. Even though the discovery of a sub gravity quantum realm, say through use of the Kalen constant k, could largely remove indeterminacy from quantum mechanics, a certain amount of uncertainty would remain. We like to think that it allows intelligent beings a certain amount of leeway in choosing their lives.

One ordinarily thinks of the evolution of space as due to the time dimension. In spite of this, I have tried to show that space and time are on an equal basis as far as change and evolution are concerned.

The big bang theory assumes that space-time is expanding spherically from a point singularity. This gives a beginning to time some 10 to 20 billion years ago. An amazing amount of work has been done on this theory. It gives a creditable evolution of matter from a very hot start to the present very cold 3 degree background temperature. But it has run into serious problems with observation, due, we believe, to certain long ingrained questionable assumptions. See our link to Questionable Cosmological Assumptions.

For one thing, we assume that space-time is not spherical but rather is an oscillating torus, that expands and contracts between two fixed limits set by a fixed radius of curvature of 3-space. In order for this doughnut metric to evolve as we suggest, time must also be three dimensional. This makes space-time six dimensional; or rather ten dimensional when one considers the four compacted force dimensions.

This geometry is complicated but easier to picture than ten dimensional string theory. See Figures 7 and 8 in our figures link, a page of the kalenuniverse.com web site.

If the time and space dimensions are much the same, why is three-space so obvious while the time dimensions are hidden?

One reason is that most of the space flows (motions) along the time dimensions are instantaneous through wormholes

In order to see how this comes about, the reader should understand our concept of the Shadow World.

The idea of a shadow world has been around for a long time. String theorists predict that all the particles have a mirror image partner that is too heavy to detect. Also their E8 x E8 super symmetry seems to predict an invisible duplicate Shadow World.

Actually Einstein=s idea of particles being wormhole bridges between two 3D slices of space-time is closer to our idea of a shadow world (See Einstein=s quote in the link to Quantum Weirdness in the kalen web site). We think of gravity space as being an ether like super fluid that converges upon matter producing a black wormhole at the center of any mass particle. These wormholes are instantaneous connections between any real world particle and its shadow world counterpart.

Now, because distance and time do not exist inside of a wormhole; a real world particle and its shadow world antimatter counterpart can be thought of as one particle.

Space flows generate the real world, then flow through mass and charge wormholes to create the next slice of space-time which is the shadow world. Thus, time is essentially the instantaneous flow of space through mass to the next observable slice of space-time which we call the shadow world.

In order to visualize this better, we will omit one dimension and think of space-time as three dimensional. Consider a three dimensional object such as a human body. A slice through the body would be a two dimensional picture. One can think of the whole body as a series of these pictures. Visualize each picture slice as a moving picture frame. Imagine a two dimensional observer who could see these pictures projected sequentially in time. He could combine and see them as a 3D object: The human body. The third dimension would be time to this 2D observer.

We see that time can be the sequential observation of our real world of three-space along the next higher dimension which we call time. We call the next slice of space-time the shadow world.

We also see how the time dimensions can be hidden in wormholes, and the shadow world hidden behind wormholes

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 Is time Travel Possible?
 by John and Mary Gribbin
In one of the wildest developments in serious science for decades, researchers from California to Moscow have recently been investigating the possibility of time travel. They are not, as yet, building TARDIS lookalikes in their laboratories; but they have realized that according to the equations of Albert Einstein’s general theory of relativity (the best theory of time and space we have), there is nothing in the laws of physics to prevent time travel. It may be extremely difficult to put into practice; but it is not impossible.

It sounds like science fiction, but it is taken so seriously by relativists that some of them have proposed that there must be a law of nature to prevent time travel and thereby prevent paradoxes arising, even though nobody has any idea how such a law would operate. The classic paradox, of course, occurs when a person travels back in time and does something to prevent their own birth -- killing their granny as a baby, in the more gruesome example, or simply making sure their parents never get together, as in Back to the Future. It goes against commonsense, say the skeptics, so there must be a law against it. This is more or less the same argument that was used to prove that space travel is impossible.

So what do Einstein’s equations tell us, if pushed to the limit? As you might expect, the possibility of time travel involves those most extreme objects, black holes. And since Einstein’s theory is a theory of space and time, it should be no surprise that black holes offer, in principle, a way to travel through space, as well as through time.

 

A simple black hole won’t do, though. If such a black hole formed out of a lump of non-rotating material, it would simply sit in space, swallowing up anything that came near it. At the heart of such a black hole there is a point known as a singularity, where space and time cease to exist, and matter is crushed to infinite density. Thirty years ago, Roger Penrose (now of Oxford University) proved that anything which falls into such a black hole must be drawn into the singularity by its gravitational pull, and also crushed out of existence.

But, also in the 1960s, the New Zealand mathematician Roy Kerr found that things are different if the black hole is rotating. A singularity still forms, but in the form of a ring, like the mint with a hole. In principle, it would be possible to dive into such a black hole and through the ring, to emerge in another place and another time. This "Kerr solution" was the first mathematical example of a time machine, but at the time nobody took it seriously. At the time, hardly anybody took the idea of black holes seriously, and interest in the Kerr solution only really developed in the 1970s, after astronomers discovered what seem to be real black holes, both in our own Milky Way Galaxy and in the hearts of other galaxies.

This led to a rash of popular publications claiming, to the annoyance of many relativists, that time travel might be possible. In the 1980s, though, Kip Thorne, of CalTech (one of the world’s leading experts in the general theory of relativity), and his colleagues set out to prove once and for all that such nonsense wasn’t really allowed by Einstein’s equations.

 

They studied the situation from all sides, but were forced to the unwelcome conclusion that there really was nothing in the equations to prevent time travel, provided (and it is a big proviso) you have the technology to manipulate black holes. As well as the Kerr solution, there are other kinds of black hole time machine allowed, including setups graphically described as "wormholes", in which a black hole at one place and time is connected to a black hole in another place and time (or the same place at a different time) through a "throat".

 

Thorne has described some of these possibilities in a recent book, Black Holes and Time Warps (Picador), which is packed with information but far from being an easy read.

 

Now, Michio Kaku, a professor of physics in New York, has come up with a more accessible variation on the theme with his book Hyperspace (Oxford UP), which (unlike Thorne’s book) at least includes some discussion of the contribution of researchers such as Robert Heinlein to the study of time travel. The Big Bang, string theory, black holes and baby universes all get a mention here; but it is the chapter on how to build a time machine that makes the most fascinating reading.

"Most scientists, who have not seriously studied Einstein’s equations," says Kaku, "dismiss time travel as poppycock". And he then goes on to spell out why the few scientists who have seriously studied Einstein’s equations are less dismissive. Our favourite page is the one filled by a diagram which shows the strange family tree of an individual who manages to be both his/her own father and his/her own mother, based on the Heinlein story "All you zombies --".

 

And Kaku’s description of a time machine is something fans of Dr Who and H.G. Wells would be happy with:

[It] consists of two chambers, each containing two parallel metal plates. The intense electric fields created between each pair of plates (larger than anything possible with today’s technology) rips the fabric of space-time, creating a hole in space that links the two chambers.

Taking advantage of Einstein’s special theory of relativity, which says that time runs slow for a moving object, one of the chambers is then taken on a long, fast journey and brought back: Time would pass at different rates at the two ends of the wormhole, [and] anyone falling into one end of the wormhole would be instantly hurled into the past or the future [as they emerge from the other end].

And all this, it is worth spelling out, has been published by serious scientists in respectable journals such as Physical Review Letters (you don’t believe us? check out volume 61, page 1446). Although, as you may have noticed, the technology required is awesome, involving taking what amounts to a black hole on a trip through space at a sizeable fraction of the speed of light. We never said it was going to be easy! So how do you get around the paradoxes? The scientists have an answer to that, too. It’s obvious, when you think about it; all you have to do is add in a judicious contribution from quantum theory to the time travelling allowed by relativity theory. As long as you are an expert in both theories, you can find a way to avoid the paradoxes.

It works like this. According to one interpretation of quantum physics (there are several interpretations, and nobody knows which one, if any, is "right"), every time a quantum object, such as an electron, is faced with a choice, the world divides to allow it to take every possibility on offer. In the simplest example, the electron may be faced with a wall containing two holes, so that it must go through one hole or the other. The Universe splits so that in one version of reality -- one set of relative dimensions -- it goes through the hole on the left, while in the other it goes through the hole on the right. Pushed to its limits, this interpretation says that the Universe is split into infinitely many copies of itself, variations on a basic theme, in which all possible outcomes of all possible "experiments" must happen somewhere in the "multiverse". So there is, for example, a Universe in which the Labour Party has been in power for 15 years, and is now under threat from a resurgent Tory Party led by vibrant young John Major.

How does this resolve the paradoxes? Like this. Suppose someone did go back in time to murder their granny when she was a little girl. On this multiverse picture, they have slid back to a bifurcation point in history. After killing granny, they move forward in time, but up a different branch of the multiverse. In this branch of reality, they were never born; but there is no paradox, because in he universe next door granny is alive and well, so the murderer is born, and goes back in time to commit the foul deed!

Once again, it sounds like science fiction, and once again science fiction writers have indeed been here before. But this idea of parallel universes and alternative histories as a solution to the time travel paradoxes is also now being taken seriously by some (admittedly, not many) researchers, including David Deutsch, in Oxford.

 

Their research deals with both time, and relative dimensions in space. You could make a nice acronym for that -- TARDIS, perhaps?

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 Time travel on Agenda

by John Gribbin

CLAIMS that time travel is impossible in principle have been shown to be in error by an Israeli researcher. Amos Ori, of the Technion-Israel Institute of Technology, in Haifa, has found a flaw in the argument put forward recently by Stephen Hawking, of Cambridge University, claiming to rule out any possibility of time travel.

This is the latest twist in a story that began in the late 1980s, when Kip Thorne and colleagues at the California Institute of Technology suggested that although there might be considerable practical difficulties in constructing a time machine, there is nothing in the laws of physics as understood at present to forbid this. Other researchers tried to find flaws in the arguments of the CalTech team, and pointed in particular to problems in satisfying a requirement known as the "weak energy condition", which says that any real observer should always measure energy distributions that are positive. This rules out some kinds of theoretical time machines, which involve travelling through black holes held open by negative energy stuff.

There are also problems with time machines that involve so-called singularities, points where space and time are crushed out of existence and the laws of physics break down. But Ori has found mathematical descriptions, within the framework of the general theory of relativity, of spacetimes which loop back upon themselves in time, but in which no singularity appears early enough to interfere with the time travel, and the weak energy condition is satisfied (Physical Review Letters, vol 71 p 2517).

"At present," he says, "one should not completely rule out the possibility of constructing a time machine from materials with positive energy densities."

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 Why Time Travel is Possible
by John Gribbin

Physicists have found the law of nature which prevents time travel paradoxes, and thereby permits time travel. It turns out to be the same law that makes sure light travels in straight lines, and which underpins the most straightforward version of quantum theory, developed half a century ago by Richard Feynman.

Relativists have been trying to come to terms with time travel for the past seven years, since Kip Thorne and his colleagues at Caltech discovered -- much to their surprise -- that there is nothing in the laws of physics (specifically, the general theory of relativity) to forbid it. Among several different ways in which the laws allow a time machine to exist, the one that has been most intensively studied mathematically is the "wormhole".

 

This is like a tunnel through space and time, connecting different regions of the Universe -- different spaces and different times. The two "mouths" of the wormhole could be next to each other in space, but separated in time, so that it could literally be used as a time tunnel.

Building such a device would be very difficult -- it would involve manipulating black holes, each with many times the mass of our Sun. But they could conceivably occur naturally, either on this scale or on a microscopic scale.

The worry for physicists is that this raises the possibility of paradoxes, familiar to science fiction fans. For example, a time traveller could go back in time and accidentally (or even deliberately) cause the death of her granny, so that neither the time traveller’s mother nor herself was ever born.

 

People are hard to describe mathematically, but the equivalent paradox in the relativists’ calculations involves a billiard ball that goes in to one mouth of a wormhole, emerges in the past from the other mouth, and collides with its other self on the way in to the first mouth, so that it is knocked out of the way and never enters the time tunnel at all. But, of course, there are many possible "self consistent" journeys through the tunnel, in which the two versions of the billiard ball never disturb one another.

If time travel really is possible -- and after seven years’ intensive study all the evidence says that it is -- there must, it seems, be a law of nature to prevent such paradoxes arising, while permitting the self- consistent journeys through time. Igor Novikov, who holds joint posts at the P. N. Lebedev Institute, in Moscow, and at NORDITA (the Nordic Institute for Theoretical Physics), in Copenhagen, first pointed out the need for a "Principle of Self-consistency" of this kind in 1989 (Soviet Physics JETP, vol 68 p 439). Now, working with a large group of colleagues in Denmark, Canada, Russia and Switzerland, he has found the physical basis for this principle.

It involves something known as the Principle of least action (or Principle of minimal action), and has been known, in one form or another, since the early seventeenth century. It describes the trajectories of things, such as the path of a light ray from A to B, or the flight of a ball tossed through an upper story window. And, it now seems, the trajectory of a billiard ball through a time tunnel. Action, in this sense, is a measure both of the energy involved in traversing the path and the time taken. For light (which is always a special case), this boils down to time alone, so that the principle of least action becomes the principle of least time, which is why light travels in straight lines.

You can see how the principle works when light from a source in air enters a block of glass, where it travels at a slower speed than in air. In order to get from the source A outside the glass to a point B inside the glass in the shortest possible time, the light has to travel in one straight line up to the edge of the glass, then turn through a certain angle and travel in another straight line (at the slower speed) on to point B. Travelling by any other route would take longer.

The action is a property of the whole path, and somehow the light (or "nature") always knows how to choose the cheapest or simplest path to its goal. In a similar fashion, the principle of least action can be used to describe the entire curved path of the ball thrown through a window, once the time taken for the journey is specified.

 

Although the ball can be thrown at different speeds on different trajectories (higher and slower, or flatter and faster) and still go through the window, only trajectories which satisfy the Principle of least action are possible.

 

Novikov and his colleagues have applied the same principle to the "trajectories" of billiard balls around time loops, both with and without the kind of "self collision" that leads to paradoxes. In a mathematical tour de force, they have shown that in both cases only self-consistent solutions to the equations satisfy the principle of least action -- or in their own words,

"the whole set of classical trajectories which are globally self-consistent can be directly and simply recovered by imposing the principle of minimal action"

(NORDITA Preprint, number 95/49A).

The word "classical" in this connection means that they have not yet tried to include the rules of quantum theory in their calculations. But there is no reason to think that this would alter their conclusions. Feynman, who was entranced by the principle of least action, formulated quantum physics entirely on the basis of it, using what is known as the "sum over histories" or "path integral" formulation, because, like a light ray seemingly sniffing out the best path from A to B, it takes account of all possible trajectories in selecting the most efficient.

So self-consistency is a consequence of the Principle of least action, and nature can be seen to abhor a time travel paradox. Which removes the last objection of physicists to time travel in principle -- and leaves it up to the engineers to get on with the job of building a time machine.

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 Time Travel for beginners

by John Gribbin

Exactly one hundred years ago, in 1895, H. G. Wells classic story The Time Machine was first published in book form. As befits the subject matter, that was the minus tenth anniversary of the first publication, in 1905, of Albert Einstein’s special theory of relativity. It was Einstein, as every schoolchild knows, who first described time as "the fourth dimension" -- and every schoolchild is wrong. It was actually Wells who wrote, in The Time Machine, that,

"there is no difference between Time and any of the three dimensions of Space, except that our consciousness moves along it"

Since the time of Wells and Einstein, there has been a continuing literary fascination with time travel, and especially with the paradoxes that seem to confront any genuine time traveller (something that Wells neglected to investigate). The classic example is the so- called "granny paradox", where a time traveller inadvertently causes the death of his granny when she was a small girl, so that the traveller’s mother, and therefore the traveller himself, were never born. In which case, he did not go back in time to kill granny . . . and so on.

A less gruesome example was entertainingly provided by the science fiction writer Robert Heinlein in his story By his bootstraps (available in several Heinlein anthologies). The protagonist in the story stumbles on a time travel device brought back to the present by a visitor from the far future.

 

He steals it and sets up home in a deserted stretch of time, constantly worrying about being found by the old man he stole the time machine from -- until one day, many years later, he realises that he is now the old man, and carefully arranges for his younger self to "find" and "steal" the time machine. Such a narcissistic view of time travel is taken to its logical extreme in David Gerrold’s The Man Who Folded Himself (Random House, 1973).

Few of the writers of Dr Who have had the imagination actually to use his time machine in this kind of way. It would, after all, make for rather dull viewing if every time the Doctor had been confronted by a disaster he popped into the TARDIS, went back in time and warned his earlier self to steer clear of the looming trouble. But the implications were thoroughly explored for a wide audience in the Back to the Future trilogy, ramming home the point that time travel runs completely counter to common sense.

 

Obviously, time travel must be impossible. Only, common sense is about as reliable a guide to science as the well known "fact" that Einstein came up with the idea of time as the fourth dimension is to history. Sticking with Einstein’s own theories, it is hardly common sense that objects get both heavier and shorter the faster they move, or that moving clocks run slow. Yet all of these predictions of relativity theory have been born out many times in experiments, to an impressive number of decimal places. And when you look closely at the general theory of relativity, the best theory of time and space we have, it turns out that there is nothing in it to forbid time travel.

 

The theory implies that time travel may be very difficult, to be sure; but not impossible.

Perhaps inevitably, it was through science fiction that serious scientists finally convinced themselves that time travel could be made to work, by a sufficiently advanced civilization. It happened like this. Carl Sagan, a well known astronomer, had written a novel in which he used the device of travel through a black hole to allow his characters to travel from a point near the Earth to a point near the star Vega. Although he was aware that he was bending the accepted rules of physics, this was, after all, a novel.

 

Nevertheless, as a scientist himself Sagan wanted the science in his story to be as accurate as possible, so he asked Kip Thorne, an established expert in gravitational theory, to check it out and advise on how it might be tweaked up. After looking closely at the non-commonsensical equations, Thorne realized that such a wormhole through space-time actually could exist as a stable entity within the framework of Einstein’s theory.

Sagan gratefully accepted Thorne’s modification to his fictional "star gate", and the wormhole duly featured in the novel, Contact, published in 1985. But this was still only presented as a shortcut through space. Neither Sagan nor Thorne realized at first that what they had described would also work as a shortcut through time. Thorne seems never to have given any thought to the time travel possibilities opened up by wormholes until, in December 1986, he went with his student, Mike Morris, to a symposium in Chicago, where one of the other participants casually pointed out to Morris that a wormhole could also be used to travel backwards in time.

 

Thorne tells the story of what happened then in his own book Black Holes and Time Warps (Picador). The key point is that space and time are treated on an essentially equal footing by Einstein’s equations -- just as Wells anticipated. So a wormhole that takes a shortcut through spacetime can just as well link two different times as two different places. Indeed, any naturally occurring wormhole would most probably link two different times. As word spread, other physicists who were interested in the exotic implications of pushing Einstein’s equations to extremes were encouraged to go public with their own ideas once Thorne was seen to endorse the investigation of time travel, and the work led to the growth of a cottage industry of time travel investigations at the end of the 1980s and in to the 1990s.

 

The bottom line of all this work is that while it is hard to see how any civilization could build a wormhole time machine from scratch, it is much easier to envisage that a naturally occurring wormhole might be adapted to suit the time traveling needs of a sufficiently advanced civilization. "Sufficiently advanced", that is, to be able to travel through space by conventional means, locate black holes, and manipulate them with as much ease as we manipulate the fabric of the Earth itself in projects like the Channel Tunnel.

Even then, there’s one snag. It seems you can’t use a time machine to go back in time to before the time machine was built. You can go anywhere in the future, and come back to where you started, but no further. Which rather neatly explains why no time travelers from our future have yet visited us -- because the time machine still hasn’t been invented!

So where does that leave the paradoxes, and common sense? There is a way out of all the difficulties, but you may not like it. It involves the other great theory of physics in the twentieth century, quantum mechanics, and another favorite idea from science fiction, parallel worlds. These are the "alternative histories", in which, for example, the South won the American Civil War (as in Ward Moore’s classic novel Bring the Jubilee), which are envisaged as in some sense lying "alongside" our version of reality.

According to one interpretation of quantum theory (and it has to be said that there are other interpretations), each of these parallel worlds is just as real as our own, and there is an alternative history for every possible outcome of every decision ever made. Alternative histories branch out from decision points, bifurcating endlessly like the branches and twigs of an infinite tree. Bizarre though it sounds, this idea is taken seriously by a handful of scientists (including David Deutsch, of the University of Oxford). And it certainly fixes all the time travel paradoxes.

On this picture, if you go back in time and prevent your own birth it doesn’t matter, because by that decision you create a new branch of reality, in which you were never born. When you go forward in time, you move up the new branch and find that you never did exist, in that reality; but since you were still born and built your time machine in the reality next door, there is no paradox.

Hard to believe? Certainly. Counter to common sense? Of course. But the bottom line is that all of this bizarre behavior is at the very least permitted by the laws of physics, and in some cases is required by those laws.

 

I wonder what Wells would have made of it all.
 

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