Space - Time
Kalen J. Craig
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 Planckís 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
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 (Einsteinís 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
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
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
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
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 180ļ rotation and multiplying by √(-1) gives a 90ļ
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
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
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
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
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
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 Einsteinís
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 Einsteinís 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 Einsteinís 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 wonít 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
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 worldís
leading experts in the general theory of relativity), and his
colleagues set out to prove once and for all that such nonsense
wasnít really allowed by Einsteinís 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 Thorneís 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 Einsteinís
equations," says Kaku, "dismiss time travel as poppycock". And he
then goes on to spell out why the few scientists who have seriously
studied Einsteinís 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 Kakuís 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 todayís technology) rips
the fabric of space-time, creating a hole in space that links the
Taking advantage of Einsteinís 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 donít 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. Itís 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?
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
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."
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 travellerís mother nor herself was ever born. People are hard
to describe mathematically, but the equivalent paradox in the
relativistsí 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 yearsí
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
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
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
"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
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.
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 Einsteinís 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 travellerís 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 Gerroldís 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
Einsteinís 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
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 spacetime actually could exist as a stable entity within the
framework of Einsteinís theory.
Sagan gratefully accepted Thorneís 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 Einsteinís 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
Einsteinís 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 travelling 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, thereís one snag. It seems you canít 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 travellers from
our future have yet visited us -- because the time machine still
hasnít 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 favourite 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
Mooreís 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 doesnít 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 behaviour 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