Time Travel Research Center © 1998 Cetin BAL - GSM:+90  05366063183 - Turkey / Denizli 

           Monday, June 24th 2002. Reading: Cosmic Perspective Chapters S3 & 17

Relativity

Recall that with Special Relativity we had two basic rules from which all the strange effects of relativity resulted:

1. The laws of physics are the same for everyone. All free floating frames of reference are indistinguishable from one another.
2. The speed of light is a constant, and measured to be the same for everyone despite their relative velocities.

General Relativity

By 1915 Einstein had argued that there should be a sense of relativity that included frames of reference that are accelerating. Hence he was able to include gravity in his new theory.

The Equivalence Principle

In special relativity we saw that when two people move relative with respect to one another at constant velocity they can each consider themselves to be at rest with equal validity.

When accelerations are involved the situation takes on another face altogether.

Imagine that You and Jackie are floating around in space and You suddenly fire your engines and produce an acceleration up at 9.8 m/s/s. You cannot consider yourself to be at rest while Jackie accelerates away from You. You feel weight and can see that Jackie is floating freely. You should also be floating free if You are not in motion and she should feel weight if she were accelerating. It would certainly seem that there is no relativity here. But Einstein thought that the laws of physics should be the same for all observers no matter if they are feeling forces or not.

In 1907 Einstein came upon a great revelation. Whenever you feel weight (as opposed to weightlessness), you can equaly well attribute it to the effects of either acceleration or gravity. This idea is called the equivalence prinicple: The effects of gravity are exactly equivalent to the effects of acceleration.

Imagine that you are sitting in a closed room with the shades drawn. If your room was moved to outerspace and accelerated at a rate of 9.8 m/s/s you would not notice anything different. If you did physics experiments by dropping balls and so forth you would yeild the same results as you did when the room was on Earth.

Return to You and Jackie. You think that you must be accelerating upward. But You could equivalently say that your ship is at rest on the Earth's surface, perched on a cliff say, and that is why you feel weight. The reason You see Jackie freely floating is that she is falling toward the Earth. She is in freefall just like space shuttle astronauts. The physics of the two situations are exactly equivalent. So the equivalence principle allows us to state that all motion is relative. This will lead us to some startling discoveries about the nature of space and time! Some alternative phrasing of the Equivalence Principle: All accelerating frames are indistiguishable. Acceleration due to gravity is equivalent to acceleration due to other forces: gravitational mass is the same as inertial mass. Freely Floating Frames are equivalent to Freely Falling Frames.

Spacetime

The physics of the two situations above may be the same, but they sure don't look the same. Why is that? General Relativity would say that it's because we are not looking at the whole picture. We are looking at the 3-dimensional picture and ignoring the time aspect. But what we have discovered thus far with relativity is that space and time are interconnected and bound up into a 4-dimensional spacetime. We cannot see the full 4-dimensional events only their projections into 3-D. So, we must learn to "look" at the full 4-D spacetime.

Spacetime is a 4-D continuum in which the independent directions of motion are up-down, forward-back, left-right, and through time. Events occur in 3 spatial dimensions and at one point in time. In the whole continuum objects are streched out in time as well. If you were a 4-D being in this continuum you could look through time as easily as you look to your right.

In 3-D we can only see projections of 4-D. And the projections can look very different from different point of view. As an example. Imagine a book. Everyone can come measure it and agree on its dimensions. But it can be viewed in projection into 2-D as very many things.

So the heart of relativity is then that different observers are seeing different projections of 4-D spacetime into 3-D space.

"Space is different for different observers. Time is different for different observers. Spacetime is the same for everyone." - Taylor, Wheeler, Freeman.

Curvature of Spacetime

We shall discover that mass/energy causes spacetime around it to curve, and that gravity is the result of an object's path through curved spacetime. But whatever does it mean for spacetime to be curved?

We must look at lower dimensional analogies to get a feel for what this means since it is not only impossible to imagine 4-D objects, but 4-D space curved into some 5th dimension (a hyperspace).

Consider good old 2-D geometry. In a flat space with no curvature (a plane):
 

But in a space which is positively curved (like a sphere):

And in a space that is negatively curved (like a saddle):

If space can be curved and geometry is different in differently curved spaces what does motion in a straight line mean?

It means taking the shortest path.

In a curved space that is going to be a curved line. In relativity that will be a line along which you feel no net forces. A force-free frame travels on a straight line.

A Freely-Floating frame is a force-free frame, and by the equivalence principle so is a Freely-Falling frame.

So if you are falling toward the Earth you are feeling no net forces as you are in freefall, and thus you are on the shortest path toward the center of the Earth. If you wish to get to the other side of the Earth (say from some high poing way up in orbit) the shortest path would not be through the center of the Earth. (Once you pass the center of the Earth you feel a net force back toward the Earth). The shortest path is along the orbit (which also has no net forces acting on it because gravitaional acceleration and centripetal acceleration balance each other).

If we could draw what this situation looks like we could imagine that the 4-Dimensions of spacetime are compressed into a 2-D rubber sheet. An object is placed within the sheet and warps its shape. The curvature of the sheet would then be into the 3rd dimension. And we can see how the orbit would be a shorter path.

We call this an Embedding Diagram.

Gravity

From gravity's behavior we can draw embedding diagrams about a gravitating object and can describe the force of gravity as a curvature of spacetime. This is fundamentally different from the Standard Model of Quantum Mechanics which uses classical forces transmitted via Bosons. Gravity is no longer a force but the result of the presence of mass.

The strength of Gravity depends upon the amount of spacetime curvature. The amount of spacetime curvature depends on the amount of mass/energy present within.
 

Orbits are the result of objects passing through curved spacetime.

We can explain the the descrepency between the amount of precession of Mercury's orbit and the amount predicted by Newton's laws. Newton's laws assume the distance around the Sun at a given radius will behave as in plane geometry and hence overestimate the length of the orbit.

General Relativity predicts the precise amount of precession that is actually observed.

Gravitational Time Dilation

Because different observers trapped within 4-D spacetime are doomed to view only projections of it we are bound to find more strange effects from General Relativity as we did with Special Relativity.

Gravitational Lensing

Light must be seen to travel at the same speed for all observers. It can never be seen to accelerate. Therefore, it must travel force-free paths. In other words, it must always travel along straight lines through whatever kind of space it is traversing.

This will mean that light will appear to travel curved paths around massive objects. This is called Gravitational Lensing.

The image of an object will appear deflected by the gravity of the foreground object. This can lead to multiple images and even rings if the geometry of the situation is just right.

This has been observed numerous times and is now used to search for different forms of Dark Matter.

 

Gravitational Redshift

Because time runs slower near a gravitating object than it does far away from it the frequency of light escaping a gravitational well will be time-dilated.

This leads to light's frequency appearing to become lower as it escapes the gravity of an object. Hence the light appears more red and this becomes a 2nd kind of redshift: Gravitational Redshift.

Note that because the light is moving toward lower frequency (and hence longer wavelengths) it is also redshifted to lower energy:

One can alternatively think of gravitational redshift arising from the light losing energy as it climbs out of the gravitational field (similar to the way a rocket loses kinetic energy to potential energy).

Gravitational Waves

Similar to how the motion of electrical charges generate waves in magnetic and electric fields, so too would it be with the gravitational field predicted by General Relativity. These waves would travel at the speed of light and be alternating compressions and rarefactions of spacetime.

Gravitational waves have as yet never been detected, because the effect they cause is very small, and the method of detection very tricky. Detectors are currently being built and hope to see gravitaional waves coming from systems that are predicted to put out tons of waves.

Some systems are binary neutron stars in close orbit. Spacetime is warped severly about a neutron star and in a system such as this strong gravity waves are expected.

The waves carry orbital energy away from the system and would cause the binary orbit to decay to smaller and smaller sizes. By Kepler's 3rd law recall that this means a faster orbital period.

One such system: The Hulse-Taylor binary neutron star system. The decay of the orbit is observed to decrease the period precisely by the amount General Relativity predicts.

Black Holes

General Relativity also predicts the existence of Black Holes. In General Relativity a Black Hole would be an object so dense that light leaving straight away from its surface would be gravitationally redshifted infinitely. In other words, light cannot escape from a black hole.

If light cannot escape a black hole, then nothing can.

The radius at which light cannot escape from is called the Schwarzchild radius:

The more massive the object the larger the radius. To make an object a black hole you must squish all its matter inside this radius. The collapsing cores of massive stars may be crushed beneath their Schwarzchild radii when neutron degeneracy pressure fails to support them against gravity.

This surface at this radius is called the Event Horizon. It is called this because beyond this surface all events must be forever unknown.

Imagine a journey into a black hole as seen by two observers: You and Jackie

• First let's imagine you are far away from a black hole and watching Jackie decend into it. She has with her a flashing watch similar to the one before. As she approaches the black hole you will notice:
  1. The light from her watch will become redshifted.
  2. The period of the flashes will get longer.

  Time seems to slow down for her relative to you. If she stopped her decent and returned to meet you, you would find that she has experienced less time than you. The closer she is to the Event Horizon and the longer she spends there the larger the time difference would be.
   

  If she now heads back toward the Event Horizon with the intention of crossing over, you will never see her cross over. The closer she gets to the Horizon the slower her time seems to run and the more redshifted her light (hence the larger the telescope you will need). At the event horizon time is frozen. Eventually, you will either get bored and leave or die while waiting to see her cross.

• From Jackie's point of view everything in her frame is normal. She will however see light from your light-watch blueshift and the period of their flashes increase. She sees your time speed up! Crossing the event horizon would be no big deal for her, she just crosses it with little fanfare. However, before crossing she would witness the entire future history of the Universe unfold before her!

  She had better watch out, however! Tidal forces (the differential pull of gravity) would be so great over the length of her body that she will be stretched into a string. He feet are feel a much stronger gravity than her head.
  
  The effect is weaker the bigger the black hole is. She would be okay if this were a supermassive black hole like those that live in the center of galaxies.

  Once she is in that is it. We can predict based on General Relativity what the interior of a black hole might be like, but she can't come back out to tell us if it is true or not. Maybe there is a singularity at the center: a single point where all of the mass is concentrated. Pure Space may give way to pure time at certain points. There is just no way to know.

Worm Holes

Imagine taking a trip from Hawaii to South Africa. It's a long trip if you fly along the Earth's surface. But what if you tunneled directly through the Earth? You could shorten the trip considerably.
 

This is the idea behind a worm hole. It is a tunnel that connects two vastly different regions of spacetime via a short-cut through hyperspace.
 

Worm holes are only predicted to be possible. They have never been observed and some suspect that there may be no natural way for them to form. They might however be possible to construct.

Using them for space travel would be tricky. Their extreme warping of spacetime leads to a wicked gravitational force that will be tough for spacetime travellers to handle. Also theory predicts that the tunnel would close off faster than even light could travel through it (turning both mouths in black holes). Some theorists have suggested that a special class of worm holes could be made to be traversable with the use of material that creates a negative pressure inside the Worm hole. They call this material exotic matter.

One reason that some scientists think that worm holes may not be allowed to exist by the Universe is that if they exist then time travel could be possible!

Time Travel

Imagine you have a worm hole out in space. The two mouths are separated by a short distance. They are initially at rest with respect to one another. If you were to move one mouth as speed approaching light with respect to the other mouth you could create a time difference between the two mouths. Travelling down one mouth and coming out the other could be a trip either forward or backward in time depending on the direction you went!

Yikes! What if you managed to go back in time and show up at the other mouth just before you entered it. Then you decide to stop yourself in the past from going in.

Uh Oh.... PARADOX!!!!!!!!!!!!!!!!

There are three ways out of the Paradox:

1. Chronology Protection Conjecture: Put forth by Stephen Hawking. The Universe does not allow any time travel. Worm holes and all other closed timelines are impossible for some reason we have yet to uncover.
2. Predestination. Time travel is possible, but one cannot change events that have already happened or will happen. The shape of spacetime already exists and cannot be changed.
3. Parallel Universes. For every cause in the Universe there are parallel Universes created (existing in some higher dimension of universes: call it a macroverse) that have the entire spread of possible effects. The most probable effects generate the most parallel universes. We are always most likely to exist in a Universe with the most probable outcome. The past cannot be altered because in doing so we only create a new Universe which branches out from the original at the moment of time travel.

Want to read more? Check out a paper I wrote on the subject several years ago: Time Travel

A Primer On Time Travel (from issue #19)
by Damon Shavers

The idea of time travel has always been a popular and intriguing notion in books, movies, and TV, but in reality, can one really travel backward and forward in time, according to the present known laws of physics?

Paradoxes, Relativity, Light Cones, and Worldlines
The possibility of time travel depends on which model of reality is correct. In one model, man's future is predetermined, so time travel into either the past or future must also be predetermined. In the second model, man's future is unknown; he can't travel into the future, since none exists, nor into the past, since he wouldn't exist. In the third model, man chooses his future from an infinite number of existing parallel universes; he can travel into the future since all possible futures exist and into the past, since even if he alters the past, there is always an alternate future.

Because of what's known as Causality Time Paradoxes, physicists have traditionally stated a chronology principle that rules out travel into the past. The most common and well-known argument against two-way time travel has become known as the Grandfather Paradox. A time traveler ventures to the past just in time to prevent the meeting of his or her grandparents. Therefore, the time traveler would not be born, and could not possibly travel to the past to prevent the meeting. Because of this paradox, common sense tells us that if working time machines could actually be constructed, there would be a serious problem with causality. Much of the recent work in this area of physics has been directed toward resolving the conflict between causality and time travel, or proving because of causality, time travel is impossible.

But one-way travel into the future raises none of these problems. Einstein's special theory of relativity predicts that, with sufficient acceleration, an astronaut could go on a journey and return to the earth decades into the future, while physically aging only a year or two. The reason is because as one approaches the speed of light (186,000 miles per second), time for the traveler slows.

And there are ways to travel back in time and not violate causality. To do so, you have to first understand the concept of time itself, as physicists understand it. In Einstein's special and general theories of relativity, three-dimensional space is combined with time to form four-dimensional space-time. Where space consists of spatial points, space-time consists of spatio-temporal points, or events, each of which represents a particular place at a particular time. A Minkowski diagram can show this: You put three-dimensional space on the x-axis, and time on the y. Now since light is a constant, it would appear in the Minkowski diagram as a straight, 45-degree line. That is, for every one unit of space, it moves one unit of time (or x=y). Since light moves in all directions through space-time, the 45-degree angles in a three-dimensional model looks like two conjoined inverted cones. All events in the "light cone" above the x-axis is in the future, while all those below the x-axis is in the past. The vertex point of the cones (where the cones meet on the x-axis) is the immediate "here-now." (See A)

In this diagram, one's life forms a kind of four-dimensional "worm" in space-time. The tip of the worm's tail corresponds to the event of your birth, and the front of its head to the event of your death. An object, seen at any one instant, is a three-dimensional cross section of this long, thin, intricately curved worm. The line along which the worm lies is called the "worldline."

But a worldline cannot be any stray squiggle. Since nothing can travel faster than light, the worldline of a physical object must remain inside the light cone originating from any event in its past. Time increases in one direction along a worldline.

Einstein's general theory of relativity states that gravity results from the curvature of space-time caused by massive bodies. Consider heavy objects lying on a couch. The objects cause imprints or dents in the couch. Then, if you dropped some crumbs on the couch, they would move in towards the dent. The same is for space-time. Matter makes space-time bend, which in turn tells other matter how to move. Einstein said that worldlines are also affected by gravity. That is, earth's worldline goes around the sun's, which also goes around the worldline of the center of our galaxy, and so on.

But what if space-time becomes so distorted that some worldlines form closed loops (also called closed timelike curves, or CTCs)? That is, if an object, traveling through its worldline in space-time, returns to the same space-time point it started from at the moment it left. Theoretically, this could happen if there was a body massive enough to bend two points in space-time on top of itself.

Wormholes, Cosmic Strings, Tipler Cylinders
In his 1915 theory of general relativity, Einstein showed that space-time is curved, and that curvature is large in the area of very massive objects. Gravity can warp and slow time, especially in regions of large masses. If an object is dense enough, the curvature in space-time becomes nearly infinite, opening a "tunnel" that connects distant regions of space-time (two space-time points lying on top of each other). This is what physicists (and Trekkies) call a wormhole.

In 1988, a physicist at Caltech named Kip Thorne and several other scientists suggested that you could use a wormhole to travel into the past. You simply construct a wormhole tunnel 600 million miles in circumference, massing over two hundred million times that of the sun (just gather around a 1000 stars like the sun, put them together, and squeeze them within the critical Schwartzchild radius). You then "move" the one mouth of the wormhole through space at nearly the speed of light, leaving the other end stationary. You somehow quickly enter the moving end. This moving end "ages" less, but it connects back to the earlier time on the fixed end. So when you emerge from that fixed end, you'll emerge in your own past. Unfortunately, openings of wormholes can only be kept open by matter that has negative density, that is, exotic matter that weighs less than nothing.

Another way of creating a time machine is by using what's called cosmic strings. Recently, Richard Gott III of Princeton University has discovered that one can make a time machine by taking two infinitely long cosmic strings (hypothetical thin strands of energy millions of light years long that may or may not actually exist) and moving them past each other at a very high speed, manipulating it so that it would contract rapidly under its own tension (due to the Lorentz Transformations). The incredible energy density of the string curves space-time, and if one enters two sides of a loop as they pass each other at almost the speed of light, one enters the past. But to go back into the past just one year, one would need a loop containing about one half the mass energy of an entire galaxy, not to mention the fact that the contracting cosmic string would create the formation of a rotating black hole, sealing off all time travel regions. (But one could sort of fix this problem and create an opening in the black hole by inserting a wormhole into the black hole, across its event horizon [the area on the outskirts of a black hole where light is not fast enough to escape the gravitation], since the wormhole is composed of exotic matter. Still following us?)

But the easiest and most plausible time machine that can be constructed is what's known as a Tipler Cylinder. The materials may be practically "exotic" and the energy requirements enormous, but according to Dr. Frank Tipler of Tulane University in 1974, the construction of a time machine is theoretically feasible. He determined that if you somehow rotate an infinitely long massive cylinder fast enough, it would also "tip" a series of light cones into a CTC. (See B) The speed at the outer surface of the cylinder, though, would have to be greater than half the speed of light. But if something were to rotate this fast, part of it would likely collapse into a singularity - an infinitely small point of space-time, usually caused by a star collapsing under its own gravity, that has infinite mass and where the laws of physics break down. And Tipler stresses, "The stability of massive rotational bodies is questionable. The energy associated with a strong angular momentum would have to be about equal to the rest-mass energy, energy so great that the accompanying centrifugal force may tear the rotating body apart."

But do time machines already exist? Assuming that the general theory of relativity is correct, then natural CTC's or natural time machines exist. And if they do exist, then to prevent causality paradoxes would require the existence of parallel universes.

Parallel Universes
Most science fiction writers, and later, physicists, use the concept of parallel universes to avoid the paradoxes of time travel.

The Many Worlds interpretation of quantum mechanics, first proposed by Hugh Everett III in 1957, states that physical reality consists of a collection of universes called a multiverse. At each quantum event, the universe splits into a multitude of new universes, each having a different outcome for that event. Basically, the Many Worlds theory is the idea that every outcome at the quantum level really does happen. This theory is the direct result of the famous Schrodinger cat thought experiment.

In 1935, the German theorist Erwin Schrodinger illustrated a paradox to show why he thought the standard model of quantum theory was ridiculous. He suggested that a live cat and a capsule of poison gas be placed inside a box. The capsule would be broken, and the lethal poison released by a trigger mechanism controlled by the decay of a radioactive atom. The experiment would be conducted during a specified time in which there would be a precisely 50-50 chance that the atom would decay, either killing the cat or leaving the cat alive. Quantum mechanics deals with the statistics of probability, not constants or fate. So under quantum probability, the radioactive atom that could trigger the release of the poison is considered to have a wave function that is made up of equal parts of a decayed state and an undecayed state. Only when an observer sees (or measures) the state of the atom, and the survival or death of the cat become definite, is there a situation the physicist calls a "collapsing wave function."

But until someone looks into the box, both possibilities of the cat's life remains likely, in a "superimposition of states." The cat is both dead and alive at the same time. As soon as someone opens the box and checks the condition of the cat, the superposition of states collapses and either possibility becomes real. So when the universe is faced with "choices" at a basic level, it decides between them at random, according to the laws of probability. It also says that the choice is not made until the quantum event is observed. Some physicists, distraught by Shrodinger's thought experiment, came up with a "solution" - at every situation that creates a probability wave on the quantum level, the universe splits into all the universes for each outcome, but we can only experience one of them.

When one thinks about it, in reality, travel to a parallel world is not really time travel at all. So if the many quantum universes do exist, they are all parallel to each other, and there is no way to get from one to another except by going backward in time and then "up" another branch. For example, in the Back To The Future movies, when Marty McFly goes back in time, he makes a change that alters the future (his original present). His new present is now a new branch, while his original present (without him) continues on in a parallel universe. In other words, his worldline was really going down one branch of time and forward up another branch, so that he continues his life in a different quantum universe, never to return to his original universe again.

How does parallel universe resolve paradoxes? Consider the Grandfather Paradox once again. Suppose you travel back in time and accidentally kill or cause the death of your grandfather before he reaches puberty. You can't get born because your mother or father can't get born, right?

The answer to this is that in this parallel world sequence where you kill your younger grandfather, quantum wave streams result in a universe where you are not born. However, the original universe where your grandfather lived to a ripe old age and sired your mom/dad still exists, thus allowing you to be born. So Everett's version of the Many World theory of quantum mechanics allows history-changing events.

This means that there are many interlacing world histories, so that if anyone went back in time and killed their grandfather when he was a kid, it would just cause space-time to branch off into a new parallel universe that is different from the one that we know. A new generation of parallel universes is created each time a time traveler reenters the time stream.

Other pasts are waiting to be discovered. There are parallel pasts - infinite numbers of them. The past that is altered by the present is just one of many. Since, according to relativity theory, there is no such thing as absolute time, then what is present for someone could be the past or the future for another.

We aren't yet equipped with the necessary technology to herd neutron stars and build Tipler cylinders. But parallel universes and time travel do fit together along with our new understanding of time.

Illustrations by Adam Liebling
Also read: "Time & the Special Theory of Relativity" by Adam Liebling
 

FURTHER REFERENCE

Einstein: A Life. Denis Brown. John Wiley & Sons, Inc., 1996.

Einstein: The Life & Times. Ronald W. Clark. The World Publishing Group, 1971.

Paradox Lost. Paul Davies in NEW SCIENTIST, Vol. 157, No.21226, page 26; March 21, 1998.

Quantum Mechanics Near Closed Time Like Lines. David Deutsch in Physical Review D, Vol. 44, No. 10, pages 3197-3217; November 15, 1991.

Quantum Physics of Time Travel. David Deutsch and Michael Lockwood in Scientific American. Volume 270, number 3 Pages 68-74 March 1994.

Causal Loops. Michael Dummett in The Nature of Time. Edited by R. Flood and M. Lockwood. Basil Blackwell, 1986.

Relativity. Albert Einstein. Routledge Classics, 2001.

Six Not-So-Easy Pieces. Richard P. Feynman. Perseus Books, 1997.

Quantum Field Theory Constrains Transversable Wormhole Geometries. L.H. Ford and T.A. Roman in Physical Review D, Vol. 53, No. 10 pages 5496 - 5507, May 15, 1996.

Time Travel In Einstein's Universe: The Physical Possibilities of Travel Through Time. J. Richard Gott. Houghton Mifflin Company, 2001.

A Brief History of Time. Stephen Hawking. Bantam, 1988.

The Paradoxes of Time Travel. David Lewis in American Philosophical Quarterly, Vol. 13, No. 2, pages 145-152; April 1976. Reprinted in The Philosophy of Time. Edited by Robin Le Poidevin and Murtay MacBeath. Oxford University Press, 1993.

Time Machines: Time Travel In Physics, Metaphysics, And Science Fiction. Second Edition. Paul J. Nahin. AIP Press, Springer-Verlag, 1999.

Must Time Machine Construction Violate the Weak Energy Condition? Amos Ori in Physical Review Letters, Vol. 71, No. 16, pages 2517-2520; October 18, 1993.

Time: A Traveler's Guide. Clifford A. Pickover. Oxford University Press, 1998.

The Fourth Dimension: A Guided Tour of the Higher Universes. Rudy Rucker. Houghton Mifflin Company, 1984.

The ABC of Relativity. Bertrand Russell. Penguin, 1959.

Black Holes and Time Warps: Einstein's Outrageous Legacy. Kip S. Thorne. W.W. Norton, 1994.

Do the Laws of Physics Permit Closed Time Like Curves? Kip S. Thorne in Annals of the New York Academy of Sciences, Vol. 631, pages 182-193; August 1991.

Parallel Universes: The Search For Other Worlds. Fred Alan Wolf. Simon & Schuster, 1988.

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