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Section 2.1: Synchronizing Clocks
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One of the most important ideas regarding how we measure the properties of moving objects is the simultaneity of events (or lack thereof) and the synchronization of clocks. However, no description of special relativity can begin without the introduction of a reference frame in which to perform measurements. Restart. We construct a reference frame with numerous clocks placed at 1-meter increments (position is given in meters and time is given in in the time it takes light to travel one meter or 3.33 × 10−9 seconds). 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 a master clock and then slowly move every other clock into place on the spacetime lattice. This is the procedure depicted in Synchronization Procedure A. Notice that it takes some time for the animation to complete, as we transport the clocks slowly so as to not incur any significant time-dilation errors.
A second procedure is depicted in Synchronization Procedure B. We know that for every one meter a clock is displaced from a master clock, there is going to be one meter of light-travel-time (or 3.33 × 10−9 seconds) delay. We build this time delay into 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 observers2) in this reference frame agree on the simultaneity of events. These observers take into account the light travel time and it is this time that is recording in their laboratory notebooks. 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 2.3 for more details on simultaneity.
2See 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).