iSoul Time has three dimensions

Simultaneity without clocks

Watches didn’t always exist. Neither did clocks that were transportable or manufactured in large quantities. I mention this because one way to determine the simultaneity of events is to have synchronized clocks transported to multiple locations – even an endless number of locations in theory.

How can an observer determine the simultaneous events from their frame of reference? Answer: simultaneous events are observed simultaneously by an observer. But how can this be reconciled with other observers who may observe the same events as non-simultaneous?

That is the point of relativity: applying transformations to coordinates from different frames of reference so that the equations of physics are the same in all reference frames. But relativity requires a convention of simultaneity (or a demonstration of what events are simultaneous events). Since I have defined time in terms of stopwatches rather than clocks, how can simultaneity be determined?

Simultaneity is defined by a process that conforms to the following:

(1) Local simultaneity is understood as a primitive concept.

(2) Two events are simultaneous if they both begin simultaneously or both end simultaneously.

(3) If events A and B are simultaneous, and events B and C are simultaneous, then events A and C are simultaneous.

For example, local events A and B are simultaneous, and B begins simultaneously with event C, whose ending is distant; then A is simultaneous with C. The intermediate connection of B and C may be a signal, which can travel long distances. However, to know the time of the signal, there must be a simultaneous event that ends at the starting observer. That is, the signal or signals must cover a round-trip.

This situation has been noted with respect to light: the one-way speed of light is not known but the round-trip speed is. So this situation is not new.

The conclusion is that simultaneity can be defined without clocks.

For further information

Review of Max Jammer, Concepts of Simultaneity: From Antiquity to Einstein and Beyond. by Jill North, American Scientist 96 (1), 2008.

Special Relativity without One-Way Velocity Assumptions: Part I, by John A. Winnie. Philosophy of Science, Vol. 37, No. 1 (Mar., 1970), pp. 81-99.

Special Relativity without One-Way Velocity Assumptions: Part II, by John A. Winnie Philosophy of Science, Vol. 37, No. 2 (Jun., 1970), pp. 223-238.

Measures of motion

Transformations with two speeds of light

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