## Illustration 1: Synchronizing Clocks

One of the most important things about how we measure the properties of moving objects is the idea of the simultaneity of events (or lack thereof) and the synchronization of clocks.  What do we mean by the synchronization of clocks?  Restart.  It is perhaps not what you think.  We construct a reference frame with numerous clocks placed at say 1-meter increments (position is given in meters and time is given in meters).  If we did this in three dimensions we would have a cubic lattice spanning all space.  Let's simplify matters by only considering one dimension.  We want all of the clocks to be synchronized with a master clock at the origin.

One way to do this is to synchronize all of the clocks at the master clock and then slowly move each clock into place on the spacetime lattice.  This  is the procedure depicted in Synchronization Procedure A.  Notice that is takes some time for the animation to complete as we transport the clocks slowly so as to not incur any time-dilation errors.

A second procedure is depicted in Synchronization Procedure B.  We know that for every one meter a clock is displaced from the master clock, there is going to be one meter of light travel time (or  3.33 X 10-9 seconds) delay.  We build this time delay in all of our clocks, put them in place, and start them when a light pulse from the master clock reaches them.

With all of the clocks now synchronized, we can start analyzing events in this frame of reference.  We first note several properties of this and every other reference frame.

• It is of infinite extent.  While we have drawn the reference frame in only one dimension and of a finite size, it is actually three dimensional and infinite.

• All observers (so-called intelligent observers3) in the reference frame agree on the simultaneity of events.  These observers take into account the light travel time.  Since we are able to look at all of space at once in the animation, we can be considered omnipresent observers.  All observers in the reference frame agree on the simultaneity of events.  See Section 2.4 for more details on simultaneity.

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3See for example, R. E. Scherr, P. S. Shaffer, and S. Vokos, "The Challenge of Changing Deeply Held Student Beliefs about the Relativity of Simultaneity," Am. J. Phys. 70, 1238 (2002) and R. E. Scherr, P. S. Shaffer, and S. Vokos, "Student Understanding of Time in Special Relativity: Simultaneity and Reference Frames," Phys. Educ. Res., Am. J. Phys. Suppl. 69, S24 (2001).