One-way Velocity of Light, Conventionality of Simultaneity, Dimensionality, and Existence1
Vesselin Petkov (Department of Philosophy, Science College, and Liberal Arts College, Concordia University)
An important epistemological lesson can be learned from the impossibility to determine the one-way velocity of light and the immediate implication that simultaneity is conventional. The vicious circle -- to determine whether two events are simultaneous we need to know the one-way velocity of light between them, but to determine the one-way velocity of light we need to know that the two events are simultaneous -- is an indication of the need for a profound change of our views on light propagation and simultaneity.
And indeed, if we try to understand what message that vicious circle is conveying to us by analyzing the impact of the conventionality of simultaneity on the dimensionality of the world and what exists2, the result is profound. The impossibility3 to measure the one-way velocity of light demonstrates that simultaneity is conventional which is impossible in a three-dimensional world -- since a three-dimensional world (the present) is defined as everything that exists simultaneously at the moment now, a conventionality of simultaneity would mean that what exists is also a matter of convention.
In a four-dimensional world conventionality of simultaneity is trivial -- as all events of spacetime are equally existent it is really our choice which events constituting a three-dimensional cross-section (lying outside of the light cone of a given event) will be regarded as simultaneous. So the profound message of the vicious circle is: we live in a four-dimensional world in which there are only worldlines of particles and light signals; the velocity of light is just a description of light worldlines in terms of our three-dimensional language since in reality (in spacetime) light does not travel at all (if the world were three-dimensional and light were really propagating, its one-way velocity could not be conventional because Nature would "know" what is the magnitude of that velocity).
So far it seems it has not been paid close attention to the fact that conventionality of simultaneity and the dimensionality of the world are directly linked -- simultaneity is conventional in a four-dimensional world; if the world is three-dimensional, there is no conventionality of simultaneity.
According to relativity the world is not three-dimensional which implies that simultaneity is conventional. The world cannot be three-dimensional since such a world is defined in terms of (i) the pre-relativistic division of events into past present, and future and (ii) the pre-relativistic concept of absolute simultaneity -- as everything that exists simultaneously at the present moment. Due to relativity of simultaneity two observers in relative motion have different three-dimensional worlds which is possible only if these are three-dimensional cross-sections of a real four-dimensional world. It should be stressed that relativity of simultaneity is impossible in a three-dimensional world (the set of simultaneous events constituting such a world would be common to all observers in relative motion in contradiction with special relativity).
Notes:
1This paper develops an idea which is briefly discussed in Section 3 of [1].
2To my knowledge only Robert Weingard [2] linked conventionality of simultaneity and the reality of events.
3Slow transport of clocks cannot be of any help; see for instance [3] and the references there.
References:
1. V. Petkov, "Simultaneity, Conventionality, and Existence", British Journal for the Philosophy of Science 40 (1989), pp. 69-76.
2. R. Weingard, "Relativity and the Reality of Past and Future Events", British Journal for the Philosophy of Science 23 (1972), pp. 119-21.
3. A. Janis, "Conventionality of Simultaneity", Stanford Encyclopedia of Philosophy.