3. Completing the Space-Time Diagram Discussion
Description
This article is from the Relativity and FTL Travel FAQ, by Jason W. Hinson jason@physicsguy.com with numerous contributions by others.
3. Completing the Space-Time Diagram Discussion
Here we will complete the discussion of the space-time diagrams which
we began in the previous chapter. We will do this by completely comparing
the coordinates our observers have for a particular event. To make that
comparison we will need to see how the lengths which represent one unit of
space and time in the reference frame of O compare with the lengths
representing the same units in O'. The easiest way for us to do this is to
use information we have already seen--in particular, we use the fact that a
clock moving with respect to an observer seems to be running slowly to that
observer and a pole moving with respect to that observer seems to be shorter
to that observer by a factor of gamma. (Note: this was explained in Chapter
1. of this FAQ.) Understanding how to use this in the space-time diagram in
order to completely construct the two observers' coordinate systems should
give some solid insight into time dilation and length contraction in special
relativity.
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