fig. 1. Wormhole exit before move
fig. 2. Wormhole exit after move
This paper discusses the current ideas concerning the use of a wormhole to create a time machine. The proposal goes back to an idea suggested by Kip Thorne in around 1988 and popularised in his book [1] on black holes and time warps published in 1994. There have been a number of objections to this proposal based on practical issues such as :- the problem of generating or finding the wormhole, the problem of moving it and the problem of keeping the wormhole open. It is my intention to challenge the core idea behind the proposal, that is the idea that a wormhole could ever be used as a link between two different times if the wormhole initially linked regions at the same time.
I first heard of the Thorne proposal around the early 1990's, although at that time I did not know the full argument put forward by Thorne et al. My immediate objection to the idea was based on the concepts I have outlined in the section entitled Different Ages not Different Times and although I have subsequently learned more of the details the fundamental objections remains. The rest of the paper is just to clarify how the extra details do not affect my original objection.
Around late 2002 a couple of popular science journal published articles [2],[3] covering the Kip Thorne idea and this prompted me to try to formalize my ideas; this consisted of writing an e-mail to one of the offending journals ( which needless to say went unpublished - which is fair enough as that is not the purpose of such magazines ). After that I let the matter rest for a while. Then in late 2004 I finally decided to float the idea in a more public forum on the Internet. Having read the sort of viscous responses heterodox views receive from news groups I wished to avoid those; but then I discovered that Wikipedia had a talk section for its article on time travel, so I chose that. I eventually received a response from one person ( who did not agree with me ) and this helped me to clarify my argument and convinced me that I would need to generate a clear presentation of my views, complete with diagrams, and place it on the web. While doing this I searched around the web to see if I could find anyone else expressing views similar to my own - I found none. Later I did eventually locate one post [4] on the sci.physics.relativity archive that did put forward an argument remarkably similar to the first part of mine - unsurprisingly he did not receive many sensible responses.
For those without access to the original book there is an on-line [5] version of the argument by Brian J. Mendez.
The first idea that needs to be clarified is the distinction between ageing in one's own concept of time and the time in some inertial reference frame. Note that I used the term "one's own concept of time" rather that time as such; this is to allow us to talk about the time according to a clock that is not attached to an inertial reference frame ( this is usually called "proper time" ).
We will start with a thought experiment involving a traveller carrying a camera with a built-in clock ( the sort of digital camera that can put a timestamp on the picture ), and who has the obligatory twin brother who remains on Earth. The traveller takes his camera on a relativistic journey that starts in the laboratory on Earth and returns to its starting point in space, i.e. back in the laboratory on Earth ( we are ignoring the movement of the Earth relative to the rest of the galaxy etc. - if this bothers you just pretend the laboratory was built in intergalactic space ). To make the discussion comprehensible let's assume on 1st January 2000 the traveller sets off on a ten year ( Earth time ) journey in such a way that the traveller only experiences nine years elapsed time. When the traveller arrives back on Earth all the local calendars will be showing 1st Jan 2010 but the internal clock for the camera will show 1st January 2009. Now the big question. If the traveller takes a photograph of the calendar on the laboratory wall does he get a picture of the 2009 calendar or the 2010 calendar? As I see it the picture must be of the 2010 calendar - even though the camera will give it a 2009 timestamp.
Once back on Earth all the interactions will be consistent with the traveller being on Earth in 2010. If there had been some event that occurred on Earth in June 2009 the traveller will not observe that event when his own clock reaches June. So although the traveller is a different age from his twin brother, he is on Earth at the same time as him. I.e. he is in 2010 and not 2009. So merely ageing less is not the same as moving through time at a different rate.
If we now repeat the argument but this time instead of just a camera the traveller takes with him the exit mechanism of the wormhole ( why I say mechanism rather than just the exit of the wormhole should become clear in later sections ). In this case the exit mechanism will age by nine year but will be in the earth frame in 2010. The wormhole entry mechanism would have been in the Earth frame for the whole ten years and have aged ten years. So although the two mechanisms will have aged by different amounts they would still be at the same time in the Earth frame. So anyone entering the wormhole in 2010 will come out in 2010 even though a clock attached to the exit mechanism would read 2009.
One thing to note is that it makes no difference whether you look at the laboratory calendar through the laboratory or through the wormhole, both are just normal space. Even if everything in the space had aged less this would not affect the time back outside the wormhole. As will be seen later, movement of the wormhole would not affect contents of the wormhole anyway; the gravitation option would however.
Once both ends are back in the laboratory they will both progress at Earth time, but with the exit clock reading a year slow. So if on first of February 2010 you entered the wormhole you would see the exit clock reading 1st Feb 2009 but the laboratory clock reading 1st Feb 2010.
The second idea that needs to be clarified is the idea of what can move. Movement is a displacement of an object or effect through space. These two cases are different. Movement of matter through space is governed by the laws of Special and General Relativity. Movement of effects is not.
A standard trivial example of an effect not being affected by Relativity is the case of the image of a lighthouse beam projected onto a wall. If we have a lighthouse at the centre of a circular wall one light second in radius and the light revolves at one revolution per second, the movement of the beam along the wall will be over six light seconds per second, i.e. six times the speed of light.
Now let us take the movement of an effect in space itself. Imagine a massive asteroid flying though empty space at a relativistic velocity. The asteroid will be subjected to time retardation due to velocity - no problem. The mass of the asteroid will distort space around it. The distortion, in the form of a gravity well, will move along at the same velocity as the asteroid. But the space itself is not moving and we would not talk about the relativistic effect on the aging of the gravity well. It would not really mean anything to talk about space moving, as the only thing you can move relative to is space itself.
Now we finally come to wormholes. A wormhole is not an object, it is a configuration of space. A wormhole may be accompanied by some form of steering mechanism ( the "exit mechanism" referred to above ) and this would consist of matter and thus be subject to the laws of Relativity but the wormhole itself would not.
Now to consider how a wormhole can move. As we have seen from the asteroid's gravity well example effects in space can move. The movement of a wormhole would be a change in the location of the wormhole exit ( to keep this simple and relevant to the Thorne example I will stick to just moving the exit ) relative to objects fixed in space but how will this movement manifest itself. Movement of the wormhole can be seen as a movement of the exit through this hyperspace but how will this appear to an observer embedded within normal space.
fig. 1. Wormhole exit before move |
fig. 2. Wormhole exit after move |
The main thing to notice is that a wormhole is merely a distortion of space, so when a wormhole moves no space is destroyed or created. The space around point B may be distorted relative to hyperspace but the distance between A and C will appear the same to an observer in real space; any contraction of the space will be matched by an equal contraction in the observer's measuring devices.
Any object travelling from B to C to keep ahead of the wormhole will experience a time dilation effect on its aging but anyone stationery at B will be stationary relative to the reference frame and will experience no time dilation due to the motion of the wormhole exit ( there will, however, be some effect due to the curvature of the space-time at the mouth of the wormhole ). The wormhole exit mechanism will experience a relativistic effect but it is meaningless to talk of the aging effect on the wormhole exit itself.
There are still some concerns about the actual topology and geometry of the distortion of the wormhole. Regions of space just off the path of motion would fall into one side of the wormhole, move along the wall and pass out behind. Along the path itself symmetry dictates that the space would need to remain at the front of the wormhole ( as with point A in the above figures ). This would lead to major distortion and I suspect would cause considerable resistance to movement. Thus I suspect a wormhole could not actually be moved very far.
What is also not clear is what limits there are to the geometry of the wormhole. If we take the analogy of a hole through the Earth as a short cut to Australia, the higher level geometry prevents us creating an arbitrarily short hole; the shortest path is governed by the diameter of the Earth.
In the Thorne version of the experiment it is assumed that Kip and Carolee would be able to hold hands throughout the trip and thus maintain the same time frame through the wormhole. This assumes that, as seen through the wormhole, Carolee does not move relative to Kip. But as Carolee moves from point B to point C ( in the figures above ) she is moving relative to the reference frame and this movement will not be dependent on the path through which Kip observes the motion. Any attempt by Kip to keep in touch by moving the wormhole along with Carolee would fail because the space he is trying to avoid will be sucked into the wormhole and still be there as seen by anyone in the reference frame; as seen from hyperspace Kip's arm will recede into the wormhole so that it will no longer reach Carolee.
Kip will see his wife receding and aging slower in the same way as anyone outside the wormhole would observe her. When she eventually return she would have aged by less, as seen along both routes ( i.e. through the wormhole and through the laboratory ), but she would still be in the present as seen by an observer in the laboratory ( different ages not different times - see above ).
If they try to keep in contact by moving around in a tiny circle instead of a straight line that would not work either. The motion would still be relative to the frame and Kip would see Carolee's age reduced ( like with particles in a synchrotron ) and the reduced aging would be the same as when observed through the laboratory. Attempting to perform the age reduction using a strong gravitation field would also fail as the two routes would still observe the same effect.
Since writing the above analysis an alternative method has occurred to me. The new method involves moving the exit of the wormhole closer to point C by shrinking the space between A and C thereby allowing Kip to keep his hand at point A while still moving relative to point C. This new situation is illustrated below.
 fig. 1. Wormhole exit before contraction |
 fig. 2. Wormhole exit after contraction |
So will this new method work?
Special relativity is concerned with the movement of objects relative to an inertial reference frame; movement of objects relative to each other due to the contraction and expansion of space to do count. If you need convincing of this try a simple thought experiment. Start with two twins close to each other and then perform a rapid symmetric expansion followed by contraction of the space between them. You have now generated a genuine symmetrical twins paradox. There is a recent Scientific American article discussing the problems associated with applying special relativity to expanding space [6].
So it appears there is still no way to get the time machine to work.
This sections briefly covers another concept that Kip Thorne covers in his book and that I find rather suspect. In chapter 11, entitled "What is reality", the good professor compares the curved space view of reality with a flat space alternative. The section is best summed up in the phrase on page 400: "Both viewpoints, curved spacetime and flat, give precisely the same predictions for any measurement performed".
But by considering the topology of a wormhole this can not hold. There is no way you can map a wormhole onto a flat view of spacetime. Consider an experiment in which you construct a closed sphere around a region of space containing one ( and only one ) end of a wormhole. In flat space there would be no way a particle within the sphere could ever get out of the sphere without going through the material of the sphere. But if there was a wormhole the particle could sneak past the barrier.
[1] Kip
Thorne,
Black
Holes and Time Warps: Einstein's Outrageous Legacy.
[2] Paul Davies,
How
to build a time machine, Scientific
American, September 2002
[3] Paul Davies, Seven
Wonders - 5, New Scientist, 21st
September 2002
[4] Julian Moore,
Wormholes
and time travel (a la Gott), sci.physics.relativity
[5] Bryan J. Méndez,
Time Travel:
There's No Time Like Yesterday, Web
[6] Charles H.
Lineweaver and Tamara M. Davis, Misconceptions
about the Big Bang, Scientific
American, March 2005 ( or here
)
Created: 2004-11-26
Last updated: 2006-04-22 - Added the section on the two paradigms.