8.1 What is Meant Here by Causality and Unsolvable Paradoxes (Relativity and FTL Travel)
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This article is from the Relativity and FTL Travel FAQ, by Jason W. Hinson jason@physicsguy.com with numerous contributions by others.
8.1 What is Meant Here by Causality and Unsolvable Paradoxes (Relativity and FTL Travel)
The principle of causality is fairly straight forward. According to
causality, if there is some effect which is produced by some cause, then the
cause must precede the effect. So, if for some observer (in some frame of
reference) an effect truly happens before its cause occurs, then causality
is violated for that observer. Now, recall our discussion in Section 1.1
concerning when occurrences happen in a frame of reference. There I took a
moment to explain that when I talk about the order of events in some frame
of reference, I mean their actual order, and not necessarily the order in
which they are seen. One can imagine a situation whereby I could first
receive light from the effect and later receive light from the cause.
However, This might be because the effect is simply much closer to me than
the cause (so that light takes less time to travel from the effect I
observer, and I see it first). After I take into account the time it took
the light to travel from each event, then I will find the order in which the
events truly occurred, and this will determine whether or not there is a
true violation of causality in my frame. This true violation of causality is
what I will be talking about, NOT some trick concerning when observers see
events, but a concept concerning the actual order of the events in some
frame of reference.
Now, one can argue that the idea of causality violation doesn't
necessarily destroy logic. The idea seems odd--to have an effect come first,
and then have the cause occur--but it doesn't have to produce a
self-contradictory situation. An unsolvable paradox, however, is a
self-contradictory situation. It is a situation which logically forbids
itself from being. Thus, when one shows that a particular set of
circumstances allows for an unsolvable paradox, then one can argue that
those circumstances must logically be impossible.
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