Simultaneity

Robert Howard Kroepel
Lakeside Studios
New Durham, NH USA 03855

Simultaneity

Simultaneity is defined as two or more event occurring at the same timepoint.

Simultaneity Definitions

http://en.wikipedia.org/wiki/Simultaneity

Simultaneity

Simultaneity is the property of two events happening at the same time in at least one reference frame.

* Gramatically, it means happening at the same time.
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The Oxford Dictionary of Physics
Alan Isaacs, ed.
Oxford University Press, Fourth Edition, 2000

simultaneity The condition in which two or more events occur at the same instant.

In Einstein's conception of simultaneity, an observer had to be located equidistant between two events such as two lightning strikes, and simultaneity would occur if the lightrays from the lightning strikes struck him at the same instant—at the same timepoint.

In the following representation of Einstein's conception of simultaneity, Observer O1 is at rest relative to, and equidistant from, Lightsource 1 (LS1) and Lightsource 2 (LS2), and Observer 2 (O2) is moving at velocity v relative to O1 in a straight line away from O1 and towards LS2.

At Timepoint 1, lightning strikes LS1 and LS2, and from LS1 Lightray 1 (LR1) is emitted at velocity c/186,00 mps in a straight line towards O1 while from LS2 Lightray 2 (LR2) is emitted at v in a straight line towards O1.

At Timepoint 2.6, LR2 strikes O2; O2 reports LR2 has struck him at Timepoint 2.6.

At Timepoint 3, LR1 strikes O1 and LR2 strikes O1; O1 reports LR1 and LR2  struck him at Timepoint 4 and therefore the lightning strikes on LS1 and LS2 were simultaneous.

At Timepoint 4, LR1 strikes O2; O2 reports LR1 has struck him at Timepoint 4 and the lightning strike on LS2 was not simultaneous with the lightning strike on LS1.

NOTE: The fact that O2 is moving away from LR1 means LR1 "goes past" O2's center of mass/CoM at c-v and the fact that O2 is moving towards LR2 means LR2 "goes past" O2's CoM at c+v. Einstein's conception of simultaneity depends on LR1 "going past" O2's CoM at c-v and LR2 "going past" O2's CoM at c+v.

Timepoints and Synchronized Clocks

If synchronized clocks—clocks whose time-intervals, rates of ticking, timepoints, and timelines are identical—are used for the determination of simultaneity, their timepoints are the criteria for the simultaneity of events; if cameras are attached to the clocks, and when triggered by the lightning strikes the cameras take photographs of the strikes and timestamp the photographs, then the timestamps serve as the criteria for the determination of the simultaneity of the lightning strikes regardless of the distances LS1 and LS2 are from O1 and/or O2.

In the following diagram, LS1 and LS2 are equidistant from O1 and O2 at Timepoint 1. If the timestamps for LS1 and LS2 are identical, then LS1 occurred at the same timepoint—Timepoint 1—as LS2 and LS1 occurred simultaneously with LS2.

In the following diagram, LS1 and LS2 are not equidistant from O1 and O2 at Timepoint 1. If the timestamps for LS1 and LS2 are identical, then LS1 occurred at the same timepoint—Timepoint 1—as LS2 and LS1 occurred simultaneously with LS2.

In the following diagram, LS1 and LS2 are not equidistant from O1 and O2 at Timepoint 1. If the timestamps for LS1 and LS2 are identical, then LS1 occurred at the same timepoint—Timepoint 1—as LS2 and LS1 occurred simultaneously with LS2.

In the following diagram, LS1, LS2 and LS3 are not equidistant from O1 and O2 at Timepoint 1. If the timestamps for LS1, LS2 and LS3 are identical, then LS1 and LS3 occurred at the same timepoint—Timepoint 1—as LS2 and LS1 and LS3 occurred simultaneously with LS2.

Whenever and wherever the time-intervals, rates of ticking, timepoints, and timelines of synchronized clocks are used to co-ordinate cameras to photograph and timestamp events, then the timestamped photos of events serve as proof of the simultaneity of events: those events occurring at the same timestamp are occurring at the same timepoint and are therefore simultaneous.

Thus, timestamped photos of events are the true criteria for physical evidence which serves as proof of the simultaneity of events—events which occurred at the same timestamp occurred at the same timepoint and thereby fulfill the requirement for simultaneity when simultaneity is defined as two or more events occurring at the same timepoint.

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