30 On the Causality Problem: Particle–Tachyon Collisions
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There is also a third possibility, which, inside the framework of macroscopic
theories, would be the best, namely that we have a ‘good’ relativistic field theory in
which we do not have to postulate any additional exception conditions in order to
secure causality. This could be, for example the non-linearity of the theory which
only allows for solutions that fulfil our experiences and views of causality, so that
we can better understand how our world is causally constructed. We believe that the
non-linear field theory, as formulated by the sine-Gordon equation, could indeed be
such a ‘good’s relativistic field theory without actually being able to prove this. If
we accept this assumption, we come to the following statement at the end of our
discussion:
The totality of the solutions of the sine-Gordon equation defines the principles of a Special
Theory of Relativity with causality preserved.
337
There is also a third possibility, which, inside the framework of macroscopic
theories, would be the best, namely that we have a ‘good’ relativistic field theory in
which we do not have to postulate any additional exception conditions in order to
secure causality. This could be, for example the non-linearity of the theory which
only allows for solutions that fulfil our experiences and views of causality, so that
we can better understand how our world is causally constructed. We believe that the
non-linear field theory, as formulated by the sine-Gordon equation, could indeed be
such a ‘good’s relativistic field theory without actually being able to prove this. If
we accept this assumption, we come to the following statement at the end of our
discussion:
The totality of the solutions of the sine-Gordon equation defines the principles of a Special
Theory of Relativity with causality preserved.