All the ways I have discussed so far of getting closed time loops
have involved warping spacetime around a spinning mass. There
is an alternative way that does not involve travelling round a
dense massive object, but requires a wormhole instead. Soon after
Kip Thorne had shown his friend Carl Sagan how a traversable
wormhole might be constructed so as to connect two distant
regions of space via a short tunnel, it was pointed out by colleagues
that there would be no reason why the wormhole should not also
join two different times. After all, it is 4D spacetime that the
wormhole is being created in, not 3D space by itself. A simpleminded
way of visualizing this is by using the block universe
model. Figure 9.2 shows a wormhole through this 3D spacetime
which connects two different times. An important point to note
here is that the throat of the wormhole is not actually imbedded
within the block, but exists in some higher dimensional space
outside the three dimensions in which it is drawn. Unfortunately,
I ran out of dimensions. But at least it gives you a rough idea
what is involved. If your ‘now’ happened to be at the LATER
TIME then travelling through the wormhole would take you into
the past. But, equally, someone whose ‘now’ was in the EARLIER
TIME would use the wormhole to travel into the future.
The way I have drawn the wormhole in the block universe
suggests that its two mouths open up in specific slices through the
block. This might imply that someone whose ‘now’ is on a slice
half way between the two will not see any wormhole mouths. In
fact, all slices that come after the EARLIER TIME slice will also
contain its wormhole mouth, since they are just that slice at later
times. All slices after the LATER TIME slice will thus contain both
wormhole mouths. One would be a link into the past and the other
to the future.
What makes the block universe model quite hard to
appreciate, but which is necessary for time travel to be possible, is
that neither time has the right to call itself the real ‘now’. Both are
equally valid since time does not move in the block universe. This
does not stop our subjective feeling that time is moving along.
So, to us living within the block universe both slices will move upwards at the same rate, along the time axis, but there will be
people whose present moments correspond to one or other of the
two times. wormhole that was not a time machine—in the sense that if you
were to go through it you would emerge at the other end at a later
time with the same amount of time having elapsed for you inside
the wormhole as had gone by on the outside—could be turned
into a time machine. What I mean by a wormhole that is not a
time machine can be understood from figure 9.2 if the EARLIER
TIME and LATER TIME slices were one and the same. Now if you
travel through the wormhole you will emerge in the same time
slice that you would be in had you not travelled through. The
trick in creating the time machine was to make use of an effect in
special relativity which you have already met. It involves the idea
behind the twins paradox.
Let me first lay out the plan for what is regarded as the easiest
way of constructing a time machine (assuming it is possible of
course):
How to build a time machine
(1) Make a wormhole (by inflating one out of the quantum foam,
or creating one from scratch by warping spacetime).
(2) Stabilize the wormhole (by keeping it open with exotic matter
or cosmic string).
(3) Electrically charge one of the wormhole mouths (so that
it can be moved about with an electric field) and load it onto a
rocket.
(4) Induce a time difference between the mouths (by flying off
at close to the speed of light with one of the mouths).
(5) Turn the wormhole into a time machine (by bringing the
mouths closer together again).
Steps (1) and (2) were discussed in the last chapter. But to
recap, we really have no idea how this could be achieved. This is
why many authors who discuss wormhole time machines usually
start glibly with the statement: “Take one traversable wormhole”.
Since I have no more to add to this I will do likewise and assume
that we already have a stable wormhole which, for convenience,
has mouths large enough for humans to walk through. The two mouths could initially be side by side in our wormhole laboratory.
Step (3) enables one of the mouths to be transported from the
wormhole laboratory and into a waiting rocket. For steps (4) and
(5) we can forget the wormhole mouth is even in the rocket. All
we need to do is have the rocket fly around at close to the speed of
light for a while and the special relativistic effect of time dilation
will do the rest.
Remember the twins paradox story? When Alice heads off
from Earth in her high speed rocket and travels around for a while
she will, on returning to Earth, find that more time has elapsed
there than she can account for. She will return younger than her
twin brother, Bob, because she has effectively fast forwarded into
the future. This time, Alice will take with her one mouth of a
wormhole and cause a time shift between the two mouths.
The following description of what this would be like is similar
to the one discussed by Kip Thorne in his book Black Holes and Time
Warps, but with some modifications. Figure 9.3(a) shows Bob in
the wormhole laboratory looking through his end of the wormhole
at Alice. Through the wormhole she is only a few metres away,
but she is in fact sitting in her rocket which can be seen outside
the window on the launch pad. Figure 9.3(b) shows the view from
Alice’s wormhole mouth which is secured inside the rocket.
Alice and Bob agree that she will fly off on a trip round the
Solar System travelling at her rocket’s cruising speed of a hundred
thousand kilometres per second (or one third of the speed of light)
and return to Earth after exactly two weeks. Let us say she departs
on a Wednesday. As she speeds away from Earth, the distance
between her and Bob through the wormhole remains constant (see
figure 9.4), even though he can see her rocket through his telescope
receding from Earth at one third of the speed of light. Bob is
able to chat to her and even pass freshly brewed cups of coffee to
her through the wormhole each morning. More importantly, they
will be counting down the days together. At all times during the
journey, their watches will be in agreement, since they make sure
they remain synchronized through the wormhole.
Two weeks later, with both Bob and Alice agreeing that it is
Wednesday, Bob watches his sister through the wormhole as she nears the end of her journey and manoeuvres her rocket through
Earth’s atmosphere before finally landing it back on its pad. Bob
goes outside to watch her land, but the sight that greets him as he
steps outside is quite a shock. The launch pad is empty, rocketless.
He pulls himself together, dashes to the observatory and aims his telescope at the patch of sky where the rocket would have come
from. Such is the resolving power of the telescope that he is able
to pick out Alice’s rocket just flying past Neptune on its journey
towards Earth. He calculates that at her current velocity she will
not reach Earth till tomorrow!
Being a scientist—he works in a wormhole laboratory after
all—it quickly dawns on Bob that this is exactly what he would
expect. He can explain what is happening by appealing to special relativity. He runs back to the wormhole laboratory to tell his
sister. Once inside, he looks through the wormhole to see Alice
just completing her final checks of the rocket’s controls and getting
ready to open the door to climb out. Hecalls throughthewormhole
congratulating her on yet another perfect landing, then proceeds
to inform her that she hasn’t actually landed yet! She waves back to him. “What do you mean I haven’t landed
yet? You just saw me land. I hope there’s some coffee waiting,
there’s something about that exotic matter in the wormhole that
really ruins coffee.”
“Wait a minute Alice,” shouts Bob a little frantically now,
“I mean it. I think you’ve moved into a different time frame to
me. I know I saw you land the rocket through the wormhole,
but out there”—he waves vaguely in the direction of the launch
pad through the window—“you are still in the outer solar system.
Your rocket is certainly not out on the launch pad. In fact, you
are not due back till tomorrow!” Alice, not surprisingly, is far
from convinced. She can see that Bob is serious, but then there
seems to be nothing illogical as far as she can see. She tries again:
“Look, we both agree that it isWednesday. In fact we’ve both been
counting off the days together. What’s more our watches are still
synchronized. Therefore we must both be in the same time frame.
And, believe me, I did just land this rocket.”
But Bob is not listening any more and is deep in thought. A
few minutes earlier he was convinced he understood why Alice
always claimedonreturning fromher travels to have beenawayfor
a shorter time than had passed by on Earth. That was just special
relativity at work. But this damned wormhole really seemed to be
screwing things up. Then, just for a moment, the fog lifts and he
understands. He starts blurting it out before he becomes confused
again.
“Alice, let’s just say that we didn’t have the wormhole. I
wouldn’t know that you had landed. In fact for me, in Earth time,
your trip really would take fifteen days and I wouldn’t see you
till tomorrow. But for you, rocket time, the journey will only take
fourteen days. Less time will have elapsed for you because of your
high speed. So you land the rocket on Wednesday according to
rocket time, but Thursday Earth time. You have moved one day
into the future.” He pauses to make sure she follows. “Go on,”
she says excitedly.
“Well, it doesn’t matter that our times are synchronized
through the wormhole. Throughout the journey, you have been
steadily dragging your wormhole mouth into the future of Earth time. I know it seems like Wednesday to you. It is, inside the
rocket. But now that you have landed back on Earth I am afraid
you have to abide by Earth time.”
“You sound like an air stewardess” she laughs. “Thank you
for flying with us, and please adjust your watches to local time,
where it is Thursday.”
“Yup. The Earth you have landed in is my tomorrow.”
“I prefer to think that I amin the present if that’s OK with you
bro.”
“Fine. If you insist on being in the present then what you see
when you look through the wormhole is one day in your past.
You are seeing a time that happened yesterday for you, when
you were still flying back. But I can equally claim to be living
in the present and I am looking through the wormhole at what
will happen tomorrow. At least I know that you will land the
rocket safely.”
“What now?” asks Alice.
“Well, the wormhole has been converted into a time machine.
Not a very versatile one I’ll admit but one which will constantly
connect two times one day apart.”
Alice and Bob can now use this two-way wormhole time
machine as often as they like. He can step through it to join his
sister in Thursday, or she can join him inWednesday. They can buy
Thursday’s newspaper, look up the previous evening’s National
Lottery result, climb back into Wednesday and pick the winning
numbers.
Of course Alice could join Bob in Wednesday and they can
then wait till Thursday, and both go outside and watch Alice
land the rocket! The Alice in the rocket will at that moment be
chatting to Bob of Wednesday and will eventually climb through
the wormhole to join her brother and become the Alice waiting
outside. So for a while there will be two Alices. Presumably
had Alice looked out of the rocket before she climbed through
the wormhole she would have seen herself, and another Bob.
I have deliberately avoided any time travel paradoxes in this
story. But if you are looking for trouble, they are very easy to find.
To give you an example, what would happen if the Alice and Bob who are standing outside watching the rocket land on Thursday
were to go over to it and climb aboard (from outside the rocket
and not via the wormhole), and attempt to stop the Alice in the
rocket from going through the wormhole? Not only must they fail
because she does go through, but they cannot even make contact
with Rocket Alice since Outside Alice has no memory of such an
encounter with herself when she was Rocket Alice!
This is just the no choice paradox rearing its ugly head, and
we must appeal to one or other of the two methods of resolving it
that I discussed in Chapter 7:
(a) If Outside Alice cannot remember seeing herself when she
was in the rocket then she will clearly be forbidden (somehow)
from interacting in any way with Rocket Alice. Physicists refer to
such a scenario as an inconsistent solution.
(b) The Universe splits into two the moment the wormhole
becomes a time machine.
You may well have taken the above delicious nonsense with a large
dose of salt. However, I should point out that not only does my
story nowhere violate any laws of physics, but too much salt is
bad for you, and ruins the flavour. So how likely is it that such a
scenario could become a reality in the distant future?
As I explained at the end of the last chapter, steps (1) and (2)
in the ‘How to build a time machine’ box may never be realized
anyway. But if they are and we can make a stable traversable
wormhole, are there any other obstacles?
Step (4), which involves inducing a time shift between the
two wormhole mouths by moving them apart at very high speed,
is only a problem if you do not think it will ever be possible to build
a rocket that can travel at near light speed. Of course that is not the
only way to induce the time shift. We could, if we had access to a
strong enough gravitational field, use the general relativistic time
dilation effect to slow the time down at one end of the wormhole.
This could be achieved by taking one wormhole mouth on a trip
round a black hole a few times. Of course the orbit does not need
to follow a closed time loop in this case since we do not require
the orbiting wormhole mouth to travel back in time. All we need is for time to be slowed down relative to the other mouth which is
far away from the black hole.
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