|Journal of Theoretics
Wormholes Create Unresolvable Paradoxes
Benjamin Thomas Solomon
Abstract: In the last chapter of Kip
Thorne's book "Black Holes & Time Warps, Einstein's Outrageous
Legacy," Thorne contemplates the possibility of time machines and
suggests that such machines may be theoretically impossible. I would like to
put forward an alternative approach suggesting, that just maybe, our models
of wormholes may be incorrect.
blackhole, wormhole, time.
To understand wormholes, one needs to understand the
following three concepts.
paradox: is about going
back in time to change history. A person goes back in time to kill his
mother to prevent his birth. The particular characteristic of this
problem is that, free will is in play.
Polchinski's billiard ball paradox:
is a version of the matricide paradox without the element of free
a wormhole that has been made into a time machine and place its two mouths
at rest near each other. Then, if a billiard ball is launched toward the
right mouth from an appropriate initial location, and with an appropriate
initial velocity, the ball will enter the right mouth, travel backward in
time, and fly out of the left mouth before it entered the right (as seen
by you and me outside the wormhole), and it will then hit its younger
self, thereby preventing itself from ever entering the right mouth and
hitting itself." (Kip S. Thorne)
trajectory: is that
trajectory of the billiard ball, different from Polchinski's paradoxical
trajectory, such that when the “old?billiard ball hits its young
self, causing its young self to enter the right mouth of the wormhole
and complete the Polchinski's billiard ball scenario in a
non-paradoxical manner - that of the old billiard ball exiting the left
mouth of the wormhole colliding with its young self and causing its
young self to enter the right mouth of the wormhole and . . . .
II. THOUGHT EXPERIMENT
By using Polchinski's paradox, with the
Echeverria-Klinhammer trajectory one is able to conduct a recursive
experiment as follows,
now is 12:00 noon. Set-up the billiard ball and let lie for a given time
period, say 10 hours, until 10.00 p.m.
the two wormhole mouths so that the returning “old?ball, exits from
the left mouth of the wormhole at time “T.?For starting conditions,
let T = 9:55 p.m.
billiard ball experiment using the Echeverria-Klinhammer trajectory.
ball exits the left wormhole mouth.
soon as “old?ball is detected, the wormhole machine is to adjust
itself so that T is decremented by time “t.?Say is t=5 minutes.
That is, T = T ?t = T - 5 minutes.
(Prior to first collision, T= 9:55 p.m., prior to second
collision, T= 9:50 p.m., prior to third collision, T=9:45p.m., prior to
fourth collision, T=9:40p.m., and so on.
ball collides with its “young?self, causing its “young?self to
enter the right wormhole mouth.
after collision, collect “old?ball in basket by allowing it to roll
off the table into a basket (and avoid introducing free will).
This experiment is a self-replicating nested loop
(typical stuff of programmers) which is bounded by 12:00 noon and 10:00 p.m.
because the Echeverria-Klinhammer trajectory does not physically exists for
collision to occur outside this time period.
I had originally thought that by the end of the
experiment there would be 120 billiard balls, and that was the end of this
story, but there is another option.
III. UNRESOLVABLE PARADOXES
Let’s make the billiard balls very small, almost
point size, and also make them very dense. Reduce the scale, “x? of the
experiment to almost microscopic level so that the Echeverria-Klinhammer
trajectory is preserved. Decrement “t?to almost zero. Then, we see that
as “x?and “t?approach zero, the number of billiard balls
collected, approaches infinity. Nothing is wrong with this just yet.
The problem is that since the mass of the mouths of the
wormholes are conserved and assuming that both wormhole mouths have finite
mass, at some point in the experiment the left mouth will attain a negative
Morris, Yurtsever, and Thorne introduced the conjecture
that there be “no unresolvable paradoxes?(Thorne). For an idea to have
some degree of success in the practical world there cannot be
inconsistencies in the logical outcomes of the proposed idea. In the case of
the time machine, we see that the logical outcome of the time machine
concept is the breakdown in the law of conservation of mass, the first unresolvable
paradox, unless negative mass is allowed.
If conservation of mass applies to both wormhole mouths
together, and their masses are transferable, then the left wormhole mouth
will never reach negative mass. But this, however, raises another question.
How many balls are there in the basket and at what time?
You will note that the number of balls in the basket,
soon after the experiment is started at 12:00+ p.m., will approach infinity,
if the experiment is “started?at 10:00 p.m.. It will be zero if the
experiment is not started. That is cause and effect, though they are bound
together, they are reversed in time. Cause occurs after the effect is
observed. This is the second unresolvable paradox. At this time, I am not
willing to accept the hypothesis that cause can occur after the effect.
The third unresolvable paradox is "What can I
do?" That is, if the basket fills up with billiard balls before I set
off the experiment, can I choose not to set off the experiment? More
programmers' stuff - a nested loop within a nested loop.
Time travel can only be possible if we can prove,
without unresolvable paradoxes, an effect prior to cause, for any case
within the boundaries defined by the wormhole mechanics. The example above
shows that this is not possible with our current understanding of space-time.
“Our current understanding?is the crux of the
issue here. Let’s explore options in an unbounded manner. One possible
explanation is that the wormholes mechanics are not correct. It might be
mathematically correct and yet not be the correct model of the universe. If
we start with the axiom that there is no past or future, only the present,
then wormholes will always return us to the present. We observe the past
only because the fastest signals, light, take time to travel across vast
distances. What is happening
“now? in that vast distance is different from what we are observing
“now.?span style="mso-spacerun: yes">
In order for any theory of time travel to be viable we
must first resolve any paradoxes or at least expose them as not being
paradoxes. Only then can we develop any plausible theory of time
travel. I hope that this paper has helped to lead us in that
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