# Special Relativity and Absolute Simultaneity

Collected papers by J. H. Field MA, D.Phil

# Special Relativity and Absolute Simultaneity

Collected papers by J. H. Field MA, D.Phil

## Absolute Simultaneity & Invariant Lengths

As is noted under The Lorentz Transformation, John Field derived the Lorentz transformation by a novel method using postulates that differ from those used by Einstein. His derivation does not require, or suggest, that differences in simultaneity arise. Similarly, it does not invoke differences in physical dimensions or distances. In his words:

"It is demonstrated that the measured spatial separation of two objects, at rest in some inertial frame, is invariant under space-time transformations. This result holds in both Galilean and Special Relativity. A corollary is that there are no 'length contraction' or associated 'relativity of simultaneity' effects in the latter theory."

Instead he suggests that what is actually taking place is a difference in velocities. This suggests that the "Reciprocity Principle" does not apply to Special Relativity. Note: The Reciprocity Principle is the idea that if object A has a velocity of v with respect to the rest frame of object B, then object B has a velocity of -v in A's rest frame. This is true in Galilean Relativity, but it is not so in Field's interpretation of Special Relativity.

The velocity of the object B in A's rest frame is actually found to be -gamma v. In conventional special relativity time dilation is explained by length contraction (which implies relativity of simultaneity) and the Reciprocity Principle is respected. In Field's approach length intervals are invariant (which follows from translational invariance, independently of the form of the transformation equations) and there is no relativity of simultaneity. Time dilation is explained by the different relative velocities in the rest frames of A and B that do not respect the Reciprocity Principle.

John Field's paper "Absolute simultaneity and invariant lengths: Special Relativity without light signals or synchronised clocks" may be viewed or downloaded here.