Using Sound to Define Simultaneity.

Propagating sound could be used to define simultaneity with respect to observers at rest in inertial reference frames S′ and S. A straight rigid rod of fixed length 2D could be oriented lengthwise, parallel to the x′-axis of S′ and the x-axis of S. The rod would have a sound emitter at each end, with a receiver at its midpoint. This apparatus could simultaneously emit two sound pulses which would propagate with the constant velocity c through some medium towards the receiver. The times between each emission and reception event would be ∆t′, ∆τ′ in S′; and ∆t , ∆τ in S as measured by a typical clock. If S′ and the rod were at rest relative to S and the medium, then: ∆t′ = ∆t = [D /c ] = ∆τ′ = ∆τ. The observers would agree that the reception events were simultaneous. If S′ and the rod and were moving at the constant velocity v (v < c) relative to S and the medium, parallel to the rod's length, then: ∆t′ = ∆t = [D /(c + v)]; ∆τ′ = ∆τ = [D /(c – v)]. The observers would agree that the reception events were not simultaneous. The formulas containing v could be used by both observers in the same experiment. This would contradict the Special Relativistic definition of simultaneity.