127 lines
7.4 KiB
Plaintext
127 lines
7.4 KiB
Plaintext
Time Travel: A Discussion
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Howard Ullman
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The possibilities of time travel have captured the imaginations of many
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people, most notably science-fiction writers. Indeed, time travel may be the
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modus operandi of plot in the science fiction genre. Time travel as a plot
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vehicle opens up wonderful avenues of exploration. However, the treatment of
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time travel in most books and movies is usually ill-conceived and poorly
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planned. Paradoxes are usually created that disturb any serious appreciation
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of the plot. In this short essay we will first examine precisely what is meant
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by the term "time travel," and will then proceed to explore the paradoxes
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associated with the concept and their resolutions.
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Time Travel: A Definition
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(N.B.: In the course of this discussion, we will use the term "time travel"
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to describe a backwards displacement in time. Forward displacements generate
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no paradoxes and can be completely described by Special and General
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Relativity.) What do we mean when we say "time travel?" Let us imagine that the
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inventor Dr. Leopold Fechner (of Tonight Show fame) has invented a "time
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machine." Using this machine, he is able to travel back in time. Dr. Fechner
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is a collection of many, many molecules. As a system of n molecules, he can be
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described at any time t by 6n variables - 3 variables describing the position
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of each molecule, and 3 variables describing the momenta of each molecule. (Of
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course, our description is bounded in precision by the Uncertainty Principle.)
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Because Dr. Fechner is only about two meters long, we may approximate reality
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and say that we may describe all his molecules existing simultaneouly at any
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time t. (Over such a short distance the effects of the Lorentz contractions
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are negligible.) When we say that Dr. Fechner as travelled back in time, we
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mean that all 6n variables at time t are "duplicated" at some time t-a. Dr.
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Fechner's molecules have disappeared at time t and have reappeared at time t-a
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in precisely the same relative configuration.
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Problem One: The Violation of The First Law
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The First Law states that the mass-energy of the universe (Ue) is constant
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(within the limits of the Uncertainty Principle.) No observer can detect a
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violation of the First Law. Now, an observer at time t-a at rest relative to
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Dr. Fechner would observe an increase in Ue of mc^2 Joules, where m is Dr.
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Fechner's rest mass in kgs. This is a very large increase in Ue. Dr.
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Fechner's trip back through time would thus violate the First Law.
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Problem Two: The Violation of The Second Law
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The Second Law states that the entropy (S) of the universe is always
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increasing at a non-negative rate. At Dr. Fechner's starting point (at time
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t), the entropy of the universe is S1. At time t-a, the entropy is S2. Now,
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S1-S2 is a positive number. Dr. Fechner would observe a decrease in the
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universe's entropy. However, there is no process which can reduce S from the
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vantage point of any observer. A machine that would reduce S by deltaS would
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increase its own entropy by deltaS+epsilon, where epsilon>0. Dr. Fechner
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would have to have an energy source "outside the universe" (a meaningless
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phrase) to cross what would appear to him as an infinite entropy barrier.
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(Recently some physicists have suggested that the Second Law does not hold when
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the effects of gravity are strong. Other physicists, however, believe the
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entropy burden is merely shifed to the space-time curvature in an as yet
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unquantified way. Needless to say, I subscribe to the latter view.)
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Problem Three: The Paradox of Causality
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This is the most popular objection to time travel. Dr. Fechner goes back in
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time and shoots his grandfather. Then he is never born, so he can't go back in
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time and shoot his grandfather, but then he IS born and DOES go back in time...
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I think a lot of the confusion comes from an outdated perspective on time.
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Most people still have the Newtonian concept fixed firmly in their minds: that
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time is a "fluid," flowing by and through us which carries everything along
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with it. The modern physicist has a much different view. Objects move in
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space as they move in time. In some sense, time simply exists. The future is
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already "there," and the past is still "there." As well, the phrase "travel
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into the past" has no meaning. There is no universal past to which one can
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travel.
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Doesn't the idea of past an future events being "there" violate quantum
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theory? In fact, relativity has no implications regarding determinism vs.
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uncertainty. As the physicist Paul Davies writes: "Does not the collapse of
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determinism conflict with the theory of relativity? In this theory there is no
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universal present, and the entire past and futue of the universe are regarded
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as existing as an indivisible whole. The world is four-dimensional (three of
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space, one of time), and all events are simply there: the future does not
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'happen' or 'unfold.' Any conflict is, in fact, illusory. Determinism
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concernes the question of whether every event is completely determined by a
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prior cause. It says nothing about whether the event is there. After all, the
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future will be what it will be regardless of whether it is determined by prior
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events or not. The four-dimensional perspective of relativity simply forbids
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us to slice up spacetime, in any absolute way, into universal instants of time.
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The notion of two events in different places being 'simultaneous' is relative
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to one's state of motion. They may be judged to occur at te same moment by on
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observer, but one moment after the other by another observer. We must
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therefore regard the universe as extended in time as well as space. But the
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theory tells us nothing about whether the temporal extension includes rigid
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links of caue and effect between the events there displayed. So in spite of
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the fact that past, present, and future seem to have no objective meaning, the
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theory of relativty does not forbid a human being fom deciding later events by
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his earlier acions. (Recall that the earlier-later ordering relation is an
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objective property of time, even though the past and the future are not.)"
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Thus, time travel presents paradoxes that cannot be resolved, even by the
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most clever author. The simple fact is that the phrase "travel back in time"
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is meaningless. Some authors may hide the holes in their arguments better, but
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all time travel descriptions have unresolvable problems.
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